Persons: Nikulin, Viacheslav Valentinovich

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Nikulin, Viacheslav Valentinovich

Total publications:	97 (88)
in MathSciNet:	87 (78)
in zbMATH:	76 (70)
in Web of Science:	53 (44)
in Scopus:	48 (46)
Cited articles:	60
Citations:	1260
Presentations:	35

Number of views:
This page:	8549
Abstract pages:	33823
Full texts:	12441
References:	2254

Professor

Doctor of physico-mathematical sciences (1985)

Speciality:

01.01.06 (Mathematical logic, algebra, and number theory)

E-mail:

, ,

Keywords:

K3 surface, Calabi–Yau manifold, mirror symmetry, Picard lattice, automorphism group, integral quadratic form, real algebraic geometry, hyperbolic reflection group, hyperbolic Kac–Moody algebra, Borcherds algebra, automorphic form.

UDC:

511.334, 512.542, 512.647.2, 512.774, 512.774.2, 512.774.4, 512.817.72, 512.818.4, 513.6, 511, 512.723, 512.817.6, 512.734, 519.46, 512.7, 512.774.5, 511.3, 511.6, 512.747, 512.647.4

Subject:

Algebraic geometry, mirror symmetry, arithmetic of quadratic forms, hyperbolic reflection groups, hyperbolic Kac–Moody algebras.

Biography

I was born 1950 in Kirov, Russia. 1965–1967, I was a student of Physical-Mathematical school No. 18 under MGU. 1967–1972, I was a student of Mechanical-Mathematical Department of MGU. 1972–1975, I was a graduate student of MIAN of Steklov under supervision by I.R. Shafarevich.

In 1977, I defended PhD thesis "Finite automorphism groups of Kahlerian K3 surfaces" (was published in 1979 in Proceed. of Moscow Math. Soc.). A general theory of such groups was constructed (especially of finite symplectic automorphism groups), and the classification of Abelian finite symplectic automorphism groups of K3 was given.

In 1979, in the paper "Integral symmetric bilinear forms and some of their geometric applications", I developed the discriminant forms technique for integral symmetric bilinear forms which became very useful in applicaitons. As geometric applications, 1) another approach to finite symplectic automorphism groups of K3 was given; 2) calculation of Milnor quadratic forms of 2-dimensional quasi-homogeneous singularities of functions was given in terms of their resolution, in application to 14 exceptional Arnolds singularities it gave an approach to Arnolds duality for them which was a first example of mirror symmetry; 3) a description of connected components of moduli of real polarized K3 surfaces was given. It is my the most cited paper (more than 100 citations by AMS Math Review).

In papers 1979–1984, I described K3 surfaces with finite automoprhism groups which is equivalent (by Global Torelli Theorem) to description of hyperbolic integral symmetric bilinear forms with automorphism groups generated by 2-reflections up to finite index. It was proved, in particular, that their number is finite in essential. For the rank 4 it was done by Vinberg.

In papers 1980–1981, I generalized above results to arbitrary arithmetic hyperbolic (in Lobachevsky spaces) reflection groups. Finiteness of the number of maximal such groups was proved in dimensions at least 10. Using the developed by me methods, later E.B. Vinberg, M.N. Prokhorov and A.G. Khovansky proved that the dimension of reflection groups in Lobachevsky spaces, with fundamental chambers of finite volume, is absolutely bounded.

In my further papers, the above methods were generalized and applied to different algebraic varieties and related polyhedra (e.g. to Mori polyhedra and nef polyhedra), to hyperbolic Kac–Moody algebras, different types of real algebraic varieties. I shall give more concrete results below.

In 1983–2008 papers, to different types of real algebraic varieties: to curves, surfaces, to description of connected components of moduli of K3 surfaces with different conditions on Picard lattices.

In 1984–2004 papers, to K3 and Enriques surfaces (automorphism groups), to Del Pezzo surfaces with log-terminal singularities, to algebraic surfaces with nef anti-canonical class, to algebraic surfaces with finite polyhedral Mori cone (finiteness results), to 3-dimensional Fano and Calabi–Yau manifolds (bounds on Picard number). Later, to some of these results, some other approaches were found which use Mori theory.

In 1995–2002 papers (most of them together with V.A. Gritsenko), to description and construction of Lorentzian (hyperbolic, generalized) Kac–Moody algebras with denominator identities which are automorphic forms (Borcherds algebras).

In 2003–2011 papers (many of them together with Carlo Madonna) methods of integral symmetric bilinear forms and discriminant forms were applied to description of cases when the moduli space of coherent sheaves with given Mukai vector on a K3 surface is isomorphic to the K3 surface itself which gives an algebraic cycle on the product of K3 with itself (or its self-correspondence).

In 2007–2011 papers, using results by Long, Maclachlan, Reid for 2-dimensional case and Agol for 3-dimensional case, and my old finiteness results and methods of 1981–1982 for arithmetic hyperbolic reflection groups in dimensions greater than 9, these finiteness results were generalized to remaining dimensions 2–8. Moreover, good bounds on ground fields were obtained which gives a hope for complete enumeration of maximal arithmetic hyperbolic refection groups.

In my last 2013 paper, the suggested by me method of 1979 to description of finite symplectic automorphism groups of K3 surfaces was generalized and specialized to concrete Niemeier lattices. This gives, in particular, description of finite symplectic automorphism groups of Kahlerian K3 surfaces together with their non-singular rational curves. This completes the classical results by Mukai, Xiao, Kondo, Hashimoto which were obtained after my 1979 paper.

Main publications:

V. Alexeev, V. V. Nikulin, Del Pezzo and $K3$ surfaces, MSJ Memoirs, 15, Mathematical Society of Japan, Tokyo, 2006 , xvi+149 pp.
V. A. Gritsenko, V. V. Nikulin, “Automorphic forms and Lorentzian Kac-Moody algebras. II”, Internat. J. Math., 9:2 (1998), 201–275
V. A. Gritsenko, V. V. Nikulin, “Automorphic forms and Lorentzian Kac-Moody algebras. I”, Internat. J. Math., 9:2 (1998), 153–199
V. V. Nikulin, “On the classification of arithmetic groups generated by reflections in Lobachevsky spaces”, Math. USSR-Izv., 18:1 (1982), 99–123
V. V. Nikulin, “Konechnye gruppy avtomorfizmov kelerovykh poverkhnostei tipa $K_3$”, Tr. MMO, 38, Izd-vo Mosk. un-ta, M., 1979, 75–137
V. V. Nikulin, “Integral symmetric bilinear forms and some of their applications”, Math. USSR-Izv., 14:1 (1980), 103–167

https://www.mathnet.ru/eng/person8383

List of publications on Google Scholar

https://zbmath.org/authors/ai:nikulin.viacheslav-v

https://mathscinet.ams.org/mathscinet/MRAuthorID/211729

https://elibrary.ru/author_items.asp?authorid=5631

https://www.webofscience.com/wos/author/record/Q-4462-2016

https://www.scopus.com/authid/detail.url?authorId=55965179900

Full list of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

1.	V. V. Nikulin, “Integral symmetric bilinear forms and some of their applications”, Math. USSR-Izv., 14:1 (1980), 103–167
2.	V. V. Nikulin, “Quotient-groups of groups of automorphisms of hyperbolic forms by subgroups generated by 2-reflections. Algebro-geometric applications”, J. Soviet Math., 22:4 (1983), 1401–1475
3.	V. A. Gritsenko, V. V. Nikulin, “Automorphic forms and Lorentzian Kac-Moody algebras. II”, Internat. J. Math., 9:2 (1998), 201–275	72 ^[x]
4.	V. V. Nikulin, “On Kummer surfaces”, Math. USSR-Izv., 9:2 (1975), 261–275
5.	V. A. Gritsenko, V. V. Nikulin, “Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras”, Amer. J. Math., 119:1 (1997), 181–224	50 ^[x]
6.	V. A. Gritsenko, V. V. Nikulin, “Igusa modular forms and 'the simplest' Lorentzian Kac–Moody algebras”, Sb. Math., 187:11 (1996), 1601–1641
7.	V. V. Nikulin, “On the classification of arithmetic groups generated by reflections in Lobachevsky spaces”, Math. USSR-Izv., 18:1 (1982), 99–123
8.	V. A. Gritsenko, V. V. Nikulin, “On classification of Lorentzian Kac–Moody algebras”, Russian Math. Surveys, 57:5 (2002), 921–979
9.	V. V. Nikulin, “On arithmetic groups generated by reflections in Lobachevskii spaces”, Math. USSR-Izv., 16:3 (1981), 573–601
10.	V. A. Gritsenko, V. V. Nikulin, “Automorphic forms and Lorentzian Kac-Moody algebras. I”, Internat. J. Math., 9:2 (1998), 153–199	30 ^[x]
11.	V. V. Nikulin, “Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces”, Izv. Math., 71:1 (2007), 53–56
12.	V. V. Nikulin, “Involutions of integral quadratic forms and their applications to real algebraic geometry”, Math. USSR-Izv., 22:1 (1984), 99–172
13.	V. V. Nikulin, “Konechnye gruppy avtomorfizmov kelerovykh poverkhnostei tipa $K_3$”, Tr. MMO, 38, Izd-vo Mosk. un-ta, M., 1979, 75–137	24 ^[x]
14.	V. A. Gritsenko, V. V. Nikulin, “$K3$ surfaces, Lorentzian Kac-Moody algebras and mirror symmetry”, Math. Res. Lett., 3:2 (1996), 211–229	20 ^[x]
15.	V. V. Nikulin, “Reflection groups in Lobachevskii spaces and the denominator identity for Lorentzian Kac–Moody algebras”, Izv. Math., 60:2 (1996), 305–334
16.	V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231–248
17.	Valery Gritsenko, Viacheslav V. Nikulin, “Lorentzian Kac–Moody algebras with Weyl groups of 2-reflections”, Proceedings of London Mathematical Society, 116:3 (2018), 485–533	17 ^[x]
18.	V. V. Nikulin, “Kählerian K3 surfaces and Niemeier lattices. I”, Izv. Math., 77:5 (2013), 954–997
19.	V. V. Nikulin, “On correspondences between K3 surfaces”, Math. USSR-Izv., 30:2 (1988), 375–383
20.	V. V. Nikulin, S. Saito, “Real $K3$ surfaces with non-symplectic involution and applications”, Proc. London Math. Soc. (3), 90:3 (2005), 591–654	13 ^[x]
21.	C. G. Madonna, V. V. Nikulin, “On a Classical Correspondence between K3 Surfaces”, Proc. Steklov Inst. Math., 241 (2003), 120–153
22.	V. V. Nikulin, “Elliptic fibrations on K3 surfaces”, Proc. Edinb. Math. Soc. (2), 57:1 (2014), 253–267	11 ^[x]
23.	V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. III”, Math. USSR-Izv., 35:3 (1990), 657–675
24.	V. V. Nikulin, “$K3$ surfaces with a finite group of automorphisms and a Picard group of rank three”, Algebraic geometry and its applications, Collection of articles, Trudy Mat. Inst. Steklov., 165, 1984, 119–142
25.	V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. II”, Math. USSR-Izv., 33:2 (1989), 355–372
26.	V. V. Nikulin, “Finite groups of automorphisms of Kählerian surfaces of type K3”, Uspekhi Mat. Nauk, 31:2(188) (1976), 223–224
27.	V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups”, Izv. Math., 79:4 (2015), 740–794
28.	V. V. Nikulin, “Weil linear systems on singular $K3$ surfaces”, Algebraic geometry and analytic geometry (1990, Tokyo), ICM-90 Satell. Conf. Proc., Springer, Tokyo, 1991, 138–164	9 ^[x]
29.	V. V. Nikulin, “On rational maps between $K3$ surfaces”, Constantin Carathéodory: an international tribute, v. II, World Sci. Publ., Teaneck, NJ, 1991, 964–995	9 ^[x]
30.	V. V. Nikulin, “On the connected components of moduli of real polarized $\mathrm K3$-surfaces”, Izv. Math., 72:1 (2008), 91–111
31.	V. V. Nikulin, “Basis of the diagram method for generalized reflection groups in Lobachevsky spaces and algebraic surfaces with nef anticanonical class”, Internat. J. Math., 7:1 (1996), 71–108	8 ^[x]
32.	V. V. Nikulin, “On factor groups of the automorphism groups of hyperbolic forms modulo subgroups generated by 2-reflections”, Sov. Math. Dokl., 20 (1979), 1156–1158
33.	V. V. Nikulin, “A remark on algebraic surfaces with polyhedral Mori cone”, Nagoya Math. J., 157 (2000), 73–92	7 ^[x]
34.	V. A. Gritsenko, V. V. Nikulin, “The arithmetic mirror symmetry and Calabi-Yau manifolds”, Comm. Math. Phys., 210:1 (2000), 1–11	7 ^[x]
35.	V. V. Nikulin, “$K3$ surfaces with interesting groups of automorphisms”, Algebraic geometry, 8, J. Math. Sci. (New York), 95:1 (1999), 2028–2048	7 ^[x]
36.	V. V. Nikulin, “The transition constant for arithmetic hyperbolic reflection groups”, Izv. Math., 75:5 (2011), 971–1005
37.	V. V. Nikulin, “A remark on discriminants of moduli of $K3$ surfaces as sets of zeros of automorphic forms”, J. Math. Sci., 81:3 (1996), 2738–2743
38.	V. V. Nikulin, “An analogue of the Torelli theorem for Kummer surfaces of Jacobians”, Math. USSR-Izv., 8:1 (1974), 21–41
39.	V. V. Nikulin, “Classification of Picard lattices of K3 surfaces”, Izv. Math., 82:4 (2018), 752–816
40.	V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. II”, Izv. Math., 80:2 (2016), 359–402
41.	V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. III”, Izv. Math., 81:5 (2017), 985–1029
42.	V. V. Nikulin, “On Correspondences of a K3 Surface with Itself. I”, Proc. Steklov Inst. Math., 246 (2004), 204–226
43.	V. V. Nikulin, “A theory of Lorentzian Kac–Moody algebras”, J. Math. Sci. (New York), 106:4 (2001), 3212–3221
44.	V. V. Nikulin, “On the Brauer group of real algebraic surfaces”, Algebraic geometry and its applications (Yaroslavl', 1992), Aspects Math., E25, Vieweg, Braunschweig, 1994, 113–136	4 ^[x]
45.	Math. Notes, 108:4 (2020), 542–549 , arXiv: 2006.03942
46.	V. V. Nikulin, “On ground fields of arithmetic hyperbolic reflection groups. III”, J. Lond. Math. Soc. (2), 79:3 (2009), 738–756	3 ^[x]
47.	V. V. Nikulin, “On Ground Fields of Arithmetic Hyperbolic Reflection Groups. II”, Mosc. Math. J., 8:4 (2008), 789–812	3 ^[x]
48.	C. G. Madonna, V. V. Nikulin, “Explicit correspondences of a K3 surface with itself”, Izv. Math., 72:3 (2008), 497–508
49.	V. V. Nikulin, “On a description of the automorphism groups of Enriques surfaces”, Sov. Math. Dokl., 30 (1984), 282–285
50.	V. V. Nikulin, “Classification of degenerations and Picard lattices of Kählerian K3 surfaces with symplectic automorphism group $D_6$”, Izv. Math., 83:6 (2019), 1201–1233
51.	V. V. Nikulin, S. Saito, “Real $K3$ surfaces with non-symplectic involution and applications. II”, Proc. Lond. Math. Soc. (3), 95:1 (2007), 20–48	2 ^[x]
52.	V. V. Nikulin, “On correspondences of a $K3$ surface with itself. II”, Algebraic geometry, Contemp. Math., 422, Amer. Math. Soc., Providence, RI, 2007, 121–172	2 ^[x]
53.	V. V. Nikulin, R. Sujatha, “On Brauer groups of real Enriques surfaces”, J. Reine Angew. Math., 444 (1993), 115–154	2 ^[x]
54.	V. A. Alekseev, V. V. Nikulin, “Classification of del Pezzo surfaces with log-terminal singularities of index $\le 2$, and involutions on K3 surfaces”, Soviet Math. Dokl., 39:3 (1989), 507–511
55.	V. V. Nikulin, “Filtrations of 2-elementary forms and involutions of integral symmetric and skew-symmetric bilinear forms”, Math. USSR-Izv., 27:1 (1986), 159–182
56.	Viacheslav V. Nikulin, “Classification of Degenerations and Picard Lattices of Kählerian K3 Surfaces with Symplectic Automorphism Group $C_4$”, Proc. Steklov Inst. Math., 307 (2019), 130–161
57.	V. A. Gritsenko, V. V. Nikulin, “Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac–Moody algebras”, Trans. Moscow Math. Soc., 78 (2017), 75–83
58.	Viacheslav V. Nikulin, “Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups”, Proc. Steklov Inst. Math., 273 (2011), 229–237
59.	V. V. Nikulin, “On ground fields of arithmetic hyperbolic reflection groups”, Groups and symmetries, CRM Proc. Lecture Notes, 47, Amer. Math. Soc., Providence, RI, 2009, 299–326	1 ^[x]
60.	V. V. Nikulin, “On the Picard number of Fano 3-folds with terminal singularities”, J. Math. Kyoto Univ., 34:3 (1994), 495–529	1 ^[x]
61.	Viacheslav V. Nikulin, Classification of degenerations and Picard lattices of Kahlerian K3 surfaces with small finite symplectic automorphism groups, 2018 , 39 pp., arXiv: 1804.00991
62.	Valery Gritsenko, Viacheslav V. Nikulin, Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac–Moody algebras, 2017 , 15 pp., arXiv: 1702.07551
63.	Viacheslav V. Nikulin, Classification of Picard lattices of K3 surfaces, 2017 , 68 pp., arXiv: 1707.05677
64.	Valery Gritsenko, Viacheslav V. Nikulin, Lorentzian Kac–Moody algebras with Weyl groups of 2-reflection, 2016 , 73 pp., arXiv: 1602.08359
65.	Viacheslav V. Nikulin, “Kählerian K3 surfaces and Niemeier lattices, II”, Adv. Stud. Pure Math., 69, 2016, 421–471
66.	V. V. Nikulin, Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, II, 2015 , 55 pp., arXiv: 1504.00326v4
67.	V. V. Nikulin, “Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups.”, Conference on K3 surfaces and related topics (KIAS, Seoul, Korea, 16–20 November), 2015 , 1 pp. http://home.kias.re.kr/MKG/h/K3surfaces/
68.	V. V. Nikulin, Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, 2014 , 70 pp., arXiv: 1403.6061v3
69.	V. V. Nikulin, “Kahlerian K3 surfaces and Niemeier lattices”, Workshop: Automorphic forms, Lie algebras and String theory (Lille University II, March 3–6), Lille, France, 2014 , 28 pp. http://www.ihes.fr/~vanhove/Lille2014/index.html
70.	V. V. Nikulin, “Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups”, Conference: Moduli spaces of real and complex varieties (Angers University, June 2–6), Angers, France, 2014 , 1 pp. http://www.math.univ-angers.fr/~mangolte/Angers-2014-abstracts.pdf
71.	V. V. Nikulin, “Kahlerian K3 surfaces and Niemeier lattices”, The 6th MSJ-SI-Development of Moduli Theory, Conference dedicated to 60th birthday of Mukai (Kyoto, RIMS, 17–21 June 2013), Research Institute of Mathematical Sciences (RIMS), Kyoto University, Japan, 2013, 1
72.	V. V. Nikulin, “Kahlerian K3 surfaces and Niemeier lattices”, Project: Mock modular forms, Moonshine and String Theory, 2013 (New York State, USA, 25 September 2013), Simons Center for Geomery and Physics, Stony Brook University, 2013, 1–1
73.	V. V. Nikulin, “Self-correspondences of $K3$ surfaces via moduli of sheaves”, Algebra, arithmetic, and geometry, in honor of Yu. I. Manin, Vol. II, Progr. Math., 270, Birkhäuser Boston Inc., Boston, MA, 2009, 439–464
74.	V. V. Nikulin, Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups, 2008 , arXiv: 0810.2945
75.	V. Alexeev, V. V. Nikulin, Del Pezzo and $K3$ surfaces, MSJ Memoirs, 15, Mathematical Society of Japan, Tokyo, 2006 , xvi+149 pp.
76.	V. V. Nikulin, “On algebraic varieties with finite polyhedral Mori cone”, The Fano Conference, Univ. Torino, Turin, 2004, 573–589
77.	C. Madonna, V. V. Nikulin, “On a classical correspondence between $K3$ surfaces. II”, Strings and geometry, Clay Math. Proc., 3, Amer. Math. Soc., Providence, RI, 2004, 285–300
78.	V. V. Nikulin, “On the Classification of Hyperbolic Root Systems of Rank Three”, Proc. Steklov Inst. Math., 230:3 (2000), 1–241
79.	V. V. Nikulin, “The diagram method for 3-folds and its application to the Kähler cone and Picard number of Calabi-Yau 3-folds. I”, Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, 261–328
80.	V. V. Nikulin, “On the topological classification of real Enriques surfaces. I”, Topology of real algebraic varieties and related topics, Amer. Math. Soc. Transl. Ser. 2, 173, Amer. Math. Soc., Providence, RI, 1996, 187–201
81.	V. A. Gritsenko, V. V. Nikulin, “Automorphic correction of a Lorentzian Kac-Moody algebra”, C. R. Acad. Sci. Paris Sér. I Math., 321:9 (1995), 1151–1156
82.	V. V. Nikulin, “Algebraic three-folds and the diagram method”, Math. USSR-Izv., 37:1 (1991), 157–189
83.	V. A. Alekseev, V. V. Nikulin, “Classification of del Pezzo surfaces with log-terminal singularities of index $\le 2$, involutions on $K3$ surfaces, and reflection groups in Lobachevskiĭ spaces”, Lectures in mathematics and its applications, 2, no. 2, Ross. Akad. Nauk, Inst. Mat. im. Steklova, Moscow; Tul'sk. Politekhn. Inst., Tula, 1988, 51–150
84.	V. V. Nikulin, “Discrete reflection groups in Lobachevsky spaces and algebraic surfaces”, Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), v. 1, 2, Amer. Math. Soc., Providence, RI, 1987, 654–671
85.	V. V. Nikulin, I. R. Shafarevich, Geometries and groups, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1987 , viii+251 pp.
86.	V. V. Nikulin, “Local invariants of 4-dimensional pseudo-Riemannian manifolds with a Lorentz metric”, J. Soviet Math., 37:4 (1987), 1210–1238
87.	V. V. Nikulin, I. R. Shafarevich, Geometrii i gruppy, Nauka, M., 1983 , 240 pp.
88.	Viacheslav V. Nikulin, “Classification of Degenerations of Codimension ${\le }\,5$ and Their Picard Lattices for Kählerian K3 Surfaces with the Symplectic Automorphism Group $(C_2)^2$”, Proc. Steklov Inst. Math., 320 (2023), 172–225
89.	F. A. Bogomolov, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (obituary)”, Russian Math. Surveys, 64:5 (2009), 939–946
90.	A. I. Kostrikin, V. S. Kulikov, Yu. I. Manin, V. V. Nikulin, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, A. N. Tyurin, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (on his 60th birthday)”, Russian Math. Surveys, 54:4 (1999), 863–868
91.	V. I. Arnol'd, O. Ya. Viro, E. A. Leontovich-Andronova, V. V. Nikulin, S. P. Novikov, O. A. Oleinik, G. M. Polotovsky, V. M. Kharlamov, “Dmitrii Andreevich Gudkov (on his seventieth birthday)”, Russian Math. Surveys, 44:1 (1989), 271–273
92.	V. A. Alexeev, C. Birkar, F. A. Bogomolov, Yu. G. Zarhin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, M. Reid, A. S. Tikhomirov, I. A. Cheltsov, “Vyacheslav Vladimirovich Shokurov (on his 70th birthday)”, Russian Math. Surveys, 76:3 (2021), 553–556
93.	F. A. Bogomolov, F. Kataneze, Yu. I. Manin, S. Yu. Nemirovskii, V. V. Nikulin, A. N. Parshin, V. V. Przhiyalkovskii, Yu. G. Prokhorov, M. Teikher, A. S. Tikhomirov, V. M. Kharlamov, I. A. Cheltsov, I. R. Shafarevich, V. V. Shokurov, “Viktor Stepanovich Kulikov (k shestidesyatiletiyu so dnya rozhdeniya)”, UMN, 68:2(410) (2013), 205–207
94.	F. A. Bogomolov, Yu. G. Zarhin, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, M. Reid, I. A. Cheltsov, “Vyacheslav Vladimirovich Shokurov (on his 60th birthday)”, Russian Math. Surveys, 65:6 (2010), 1193–1198
95.	F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605
96.	S. O. Gorchinskiy, Vik. S. Kulikov, V. V. Nikulin, D. O. Orlov, D. V. Osipov, V. L. Popov, N. A. Tyurin, G. B. Shabat, A. I. Shafarevich, V. V. Shokurov, “Igor Rostislavovich Shafarevich (on the centenary of his birthday)”, Russian Math. Surveys, 78:6 (2023), 1167–1178
97.	F. A. Bogomolov, S. O. Gorchinskiy, A. B. Zheglov, V. V. Nikulin, D. O. Orlov, D. V. Osipov, A. N. Parshin, V. L. Popov, V. V. Przyjalkowski, Yu. G. Prokhorov, M. Reid, A. G. Sergeev, D. V. Treschev, A. K. Tsikh, I. A. Cheltsov, E. M. Chirka, “Viktor Stepanovich Kulikov (on his 70th birthday)”, Russian Math. Surveys, 77:3 (2022), 555–557

Presentations in Math-Net.Ru

1.	О классификации келеровых К3-поверхностей с бесконечной группой автоморфизмов, сохраняющей эллиптический пучок К3-поверхности V. V. Nikulin Shafarevich Seminar May 17, 2022 15:00
2.	Lecture 14. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" December 7, 2021 18:00
3.	Lecture 13. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" November 30, 2021 18:00
4.	Lecture 12. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" November 23, 2021 18:00
5.	Lecture 11. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" November 16, 2021 18:00
6.	Lecture 10. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" November 9, 2021 18:00
7.	Lecture 9. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" November 2, 2021 18:00
8.	Lecture 8. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" October 26, 2021 18:00
9.	Lecture 7. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" October 19, 2021 18:00
10.	Lecture 6. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" October 12, 2021 18:00
11.	Lecture 5. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" October 5, 2021 18:00
12.	Lecture 4. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" September 28, 2021 18:00
13.	Lecture 3. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" September 21, 2021 18:00
14.	Lecture 2. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" September 14, 2021 18:00
15.	Lecture 1. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces V. V. Nikulin Course by V. V. Nikulin "Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces" September 7, 2021 18:00
16.	Classification of degenerations and Picard lattices of Kahlerian K3 surfaces with finite symplectic automorphism group V. V. Nikulin Algebraic Geometry and Arithmetic: a conference on the occasion of V.V. Nikulin 70th birthday October 22, 2020 11:00
17.	Вырождения и решетки Пикара К3-поверхностей с конечными симплектическими группами автоморфизмов V. V. Nikulin Steklov Mathematical Institute Seminar April 19, 2018 16:00
18.	Classification of Picard lattices of $K3$ surfaces V. V. Nikulin "Algebra, algebraic geometry, and number theory". Memorial conference for academician Igor Rostislavovich Shafarevich June 5, 2017 15:50
19.	Arithmetic mirror symmetry for K3 surfaces V. V. Nikulin Automorphic forms and their applications January 17, 2017 18:00
20.	Lorentzian Kac-Moody algebras and automorphic forms. Introduction V. V. Nikulin Automorphic forms and their applications September 29, 2015 18:30
21.	Classfication of degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups, II V. V. Nikulin Shafarevich Seminar June 23, 2015 13:30
22.	Классификация вырождений кэлеровых К3-поверхностей с конечными симплектическими группами автоморфизмов V. V. Nikulin Shafarevich Seminar January 20, 2015 15:00
23.	Пучки эллиптических кривых и группы автоморфизмов поверхностей K3 V. V. Nikulin International conference dedicated to the 90th anniversary of academician Igor Rostislavovich Shafarevich June 4, 2013 10:30
24.	Kahlerian K3 surfaces and Niemeier lattices V. V. Nikulin International conference "KUL!FEST" dedicated to the 60th anniversary of Vik. S. Kulikov December 5, 2012 16:00
25.	Поверхности дель Пеццо и К3 III V. V. Nikulin Summer mathematical school "Algebra and Geometry", 2012 July 31, 2012 09:30
26.	Поверхности дель Пеццо и К3 II V. V. Nikulin Summer mathematical school "Algebra and Geometry", 2012 July 29, 2012 14:30
27.	Поверхности дель Пеццо и К3 I V. V. Nikulin Summer mathematical school "Algebra and Geometry", 2012 July 26, 2012 11:30
28.	Kähler K3 surfaces and Niemeier lattices V. V. Nikulin One-day conference dedicated to the memory of V. A. Iskovskikh December 29, 2011 12:30
29.	Константа переноса для арифметических гиперболических групп отражений V. V. Nikulin Seminar by Algebra Department July 6, 2010 14:00
30.	On self-correspondences of K3 surfaces via moduli of sheaves V. V. Nikulin International conference "Geometry of Algebraic Varieties" dedicated to the memory of Vasily Alexeevich Iskovskikh June 30, 2009 16:30
31.	On classification of arithmetic groups generated by reflections in Lobachevsky spaces V. V. Nikulin International Conference of Steklov Institute Members, working outside Russia June 6, 2009 12:30
32.	Соответствия поверхности K3 с собой с помощью модулей пучков, и арифметические группы отражений V. V. Nikulin Seminar by Algebra Department April 21, 2009 15:00
33.	О явных соответствиях поверхности К3 с собой с помошью модулей пучков V. V. Nikulin Seminar by Algebra Department July 8, 2008 15:00
34.	О классификации арифметических групп, порожденных отражениями, в пространствах Лобачевского V. V. Nikulin Seminar by Algebra Department October 30, 2007 15:00
35.	Соответствия K3-поверхности с собой, с использованием вектора Мукаи общего вида V. V. Nikulin Seminar by Algebra Department January 17, 2006

Books in Math-Net.Ru

V. V. Nikulin, On the classification of hyperbolic root systems of rank three, Trudy Mat. Inst. Steklova, 230, ed. I. R. Shafarevich, E. F. Mishchenko, 2000, 256 с.
http://mi.mathnet.ru/book243

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