Persons: Batyrev, Victor Vadimovich

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Batyrev, Victor Vadimovich

Total publications:	57 (57)
in MathSciNet:	54 (54)
in zbMATH:	45 (45)
in Web of Science:	6 (6)
in Scopus:	16 (16)
Cited articles:	29
Citations:	929
Presentations:	18

Number of views:
This page:	4260
Abstract pages:	3509
Full texts:	633
References:	436

Professor

Doctor of physico-mathematical sciences

Speciality:

01.01.06 (Mathematical logic, algebra, and number theory)

E-mail:

Keywords:

algebraic varieties

UDC:

512.7, 513.6

MSC:

14M25, 14J45, 52B20

Subject:

Toric and spherical varieties, rational points on algebraic varieties, Fano varieties, Calabi-Yau varieties, mirror symmetry

Main publications:

Batyrev, V. V. and Manin, Yu. I., “Sur le nombre des points rationnels de hauteur borné des variétés algébriques”, Math. Ann., 286:1-3 (1990), 27–43
Batyrev, Victor V., “Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori”, Duke Math. J., 69:2 (1993), 349–409
Batyrev, Victor V., “Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties”, J. Algebraic Geom., 3:3 (1994), 493–535
Batyrev, Victor V. and Tschinkel, Yuri, “Manin's conjecture for toric varieties”, J. Algebraic Geom., 7:1 (1998), 15–53
Batyrev, Victor V., “Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs”, J. Eur. Math. Soc., 1:1 (1999), 5–33

https://www.mathnet.ru/eng/person25047

List of publications on Google Scholar

List of publications on ZentralBlatt

https://mathscinet.ams.org/mathscinet/MRAuthorID/219978

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. Batyrev, Ju. Manin, “Sur le nombre des points rationnels de hauteur borné des variétés algébriques”, Math. Ann., 286:1-3 (1990), 27–43	98 ^[x]
2.	V. Batyrev, D. Cox, “On the Hodge structure of projective hypersurfaces in toric varieties”, Duke Math. J., 75:2 (1994), 293–338	96 ^[x]
3.	V. Batyrev, D. Dais, “Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry”, Topology, 35:4 (1996), 901–929	79 ^[x]
4.	V. Batyrev, I. Ciocan-Fontanine, B. Kim, D. van Straten, “Mirror symmetry and toric degenerations of partial flag manifolds”, Acta Mathematica, 184:1 (2000), 1–39	68 ^[x]
5.	V. Batyrev, D. van Straten, “Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties”, Comm. Math. Phys., 168:3 (1995), 493–533	68 ^[x]
6.	V. Batyrev, I. Ciocan-Fontanine, B. Kim, D. van Straten, “Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians”, Nuclear Phys. B, 514:3 (1998), 640–666	62 ^[x]
7.	V. Batyrev, L. Borisov, “Mirror duality and string-theoretic Hodge numbers”, Invent. Math., 126:1 (1996), 183–203	61 ^[x]
8.	Victor Batyrev, “Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs”, Journal of the European Mathematical Society, 1:1 (1999), 5–33	57 ^[x]
9.	V. Batyrev, B. Nill, “Multiples of lattice polytopes without interior lattice points”, Mosc. Math. J., 7:2 (2007), 195–207	37 ^[x]
10.	V. V. Batyrev, “Toroidal Fano 3-folds”, Math. USSR-Izv., 19:1 (1982), 13–25
11.	V. Batyrev, O. Popov, “The Cox ring of a del Pezzo surface”, Arithmetic of higher-dimensional algebraic varieties (Palo Alto, CA, 2002), Progr. Math., 226, Birkhäuser Boston, Boston, MA, 2004, 85–103	33 ^[x]
12.	V. Batyrev, B. Nill, “Combinatorial aspects of mirror symmetry”, Integer points in polyhedra—geometry, number theory, representation theory, algebra, optimization, statistics, Contemp. Math., 452, Amer. Math. Soc., Providence, RI, 2008, 35–66	31 ^[x]
13.	V. Batyrev, Yu. Tschinkel, “Rational points of bounded height on compactifications of anisotropic tori”, Internat. Math. Res. Notices, 1995, no. 12, 591–635	31 ^[x]
14.	V. V. Batyrev, Yu. Tschinkel, “Height zeta functions of toric varieties”, J. Math. Sci., 82:1 (1996), 3220–3239
15.	V. Batyrev, Yu. Tschinkel, “Height zeta functions of toric varieties”, Journal of Mathematical Sciences, 82:1 (1996), 3220–3239	26 ^[x]
16.	V. Batyrev, M. Kreuzer, “Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions”, Advances in Theoretical and Mathematical Physics, 14:3 (2010), 879–898	22 ^[x]
17.	V. Batyrev, E. Selivanova, “Einstein-Kähler metrics on symmetric toric Fano manifolds”, J. Reine Angew. Math., 512 (1999), 225–236	20 ^[x]
18.	V. V. Batyrev, E. N. Materov, “Toric residues and mirror symmetry”, Mosc. Math. J., 2:3 (2002), 435–475	16 ^[x]
19.	V. Batyrev, M. Blume, “The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces”, The Tohoku Mathematical Journal. Second Series, 63:4 (2011), 581–604	13 ^[x]
20.	Victor Batyrev, Dorothee Juny, “Classification of Gorenstein toric Del Pezzo varieties in arbitrary dimension”, Mosc. Math. J., 10:2 (2010), 285–316	11 ^[x]
21.	V. Batyrev, A. Moreau, “The arc space of horospherical varieties and motivic integration”, Compositio Mathematica, 149:8 (2013), 1327–1352	10 ^[x]
22.	V. Batyrev, M. Blume, “On generalisations of Losev-Manin moduli spaces for classical root systems”, Pure Appl. Math. Q., 7:4 (2011), 1053–1084	9 ^[x]
23.	V. Batyrev, F. Haddad, “On the Geometry of $\operatorname{SL}(2)$-Equivariant Flips”, Mosc. Math. J., 8:4 (2008), 621–646	8 ^[x]
24.	V. Batyrev, K. Schaller, “Stringy Chern classes of singular toric varieties and their applications”, Commun.Num.Theor.Phys., 11 (2017), 1–40	4 ^[x]
25.	V. Batyrev, M. Kreuzer, “Integral cohomology and mirror symmetry for Calabi-Yau 3-folds”, Mirror symmetry. V, AMS/IP Stud. Adv. Math., 38, Amer. Math. Soc., Providence, RI, 2006, 255–270	4 ^[x]
26.	Victor Batyrev, “Boundedness of the degree of multidimensional toric Fano varieties”, Moscow Univ. Math. Bull., 37:1 (1982), 28–33
27.	V. V. Batyrev, K. Schaller, “Stringy $E$-functions of canonical toric Fano threefolds and their applications”, Izv. Math., 83:4 (2019), 676–697
28.	K. Altmann, V. Batyrev, B. Tessier, “Report 5/2006: Convex and Algebraic Geometry (January 29th – February 4th, 2006)”, Oberwolfach Reports, 3:1 (2006), 253–316	1 ^[x]
29.	V. V. Batyrev, “On some numerical characteristics of multidimensional Fano varieties”, Math. USSR-Izv., 26:2 (1986), 423–435
30.	Victor Batyrev, The stringy Euler number of Calabi-Yau hypersurfaces in toric varieties and the Mavlyutov duality, 2017 (Published online) , 35 pp., arXiv: 1707.02602
31.	V. Batyrev, G. Gagliardi, “On the algebraic stringy Euler number”, Proc. Amer. Math. Soc., 145 (2017), 1–13 (to appear)
32.	V. Batyrev, A. Moreau, Satellites of spherical subgroups, 2016 (Published online) , 39 pp., arXiv: 1610.07377
33.	V. Batyrev, M. Kreuzer, “Conifold degenerations of Fano 3-folds as hypersurfaces in toric varieties”, Strings, gauge fields, and the geometry behind, World Sci. Publ., Hackensack, NJ, 2013, 187–212
34.	V. Batyrev, J. Hofscheier, Lattice polytopes, finite abelian subgroups in $\operatorname{SL}(n)$ and coding theory, 2013 (Published online) , 18 pp., arXiv: 1309.5312
35.	K. Altmann, V. Batyrev, Y. Karshon, “Toric geometry. Abstracts from the workshop held April 15–21, 2012.”, Oberwolfach Reports, 9:2 (2012), 1231–1306
36.	V. Batyrev, J. Hofscheier, A generalization of a theorem of G. K. White, 2010 (Published online) , 12 pp., arXiv: 1004.3411
37.	K. Altmann, V. Batyrev, Y. Karshon, “Toric geometry. Abstracts from the workshop held January 4th – January 10th, 2009.”, Oberwolfach Reports, 6:1 (2009), 5–74
38.	Victor Batyrev, “Lattice polytopes with a given $h^*$-polynomial”, Algebraic and geometric combinatorics, 423, Amer. Math. Soc., Providence, RI, 2006, 1–10 (to appear)
39.	Victor Batyrev, “Toric degenerations of Fano varieties and constructing mirror manifolds”, The Fano Conference, Univ. Torino, Turin, 2004, 109–122
40.	V. Batyrev, E. Materov, “Mixed toric residues and Calabi-Yau complete intersections”, Calabi-Yau varieties and mirror symmetry (Toronto, ON, 2001), Fields Inst. Commun., 38, Amer. Math. Soc., Providence, RI, 2003, 3–26
41.	Victor Batyrev, “Stringy Hodge numbers and Virasoro algebra”, Mathematical Research Letters, 7:2-3 (2000), 155–164
42.	Victor Batyrev, Canonical abelianization of finite group actions, 2000 (Published online) , 4 pp., arXiv: math/0009043
43.	Victor Batyrev, “Birational Calabi-Yau $n$-folds have equal Betti numbers”, New trends in algebraic geometry (Warwick, 1996), London Math. Soc. Lecture Note Ser., 264, Cambridge Univ. Press, Cambridge, 1999, 1–11
44.	Victor Batyrev, “Mirror symmetry and toric geometry”, Documenta Mathematica, 1998, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 239–248
45.	V. Batyrev, Ju. Tschinkel, “Manin's conjecture for toric varieties”, Journal of Algebraic Geometry, 7:1 (1998), 15–53
46.	Victor Batyrev, “Stringy Hodge numbers of varieties with Gorenstein canonical singularities”, Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), World Sci. Publ., River Edge, NJ, 1998, 1–32
47.	V. Batyrev, Yu. Tschinkel, “Tamagawa numbers of polarized algebraic varieties”, Nombre et répartition de points de hauteur bornée (Paris, 1996), Astérisque, 251, Soc. Math. France, 1998, 299–340
48.	V. Batyrev, L. Borisov, “Dual cones and mirror symmetry for generalized Calabi-Yau manifolds”, Mirror symmetry, II, Amer. Math. Soc., Providence, RI, 1997, 71–86
49.	V. Batyrev, Yu. Tschinkel, “Rational points on some Fano cubic bundles”, C. R. Acad. Sci. Paris Sér. I Math., 323:1 (1996), 41–46
50.	V. Batyrev, L. Borisov, “On Calabi-Yau complete intersections in toric varieties”, Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, 39–65
51.	V. Batyrev, Yu. Tschinkel, “Rational points on toric varieties”, Number theory (Halifax, NS, 1994), CMS Conf. Proc., 15, Amer. Math. Soc., Providence, RI, 1995, 39–48
52.	Victor Batyrev, “Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties”, Journal of Algebraic Geometry, 3:3 (1994), 493–535
53.	Victor Batyrev, “Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori”, Duke Math. J., 169 (1993), 349–409
54.	Victor Batyrev, “Quantum cohomology rings of toric manifolds”, Journées de Géométrie Algébrique d'Orsay (Orsay, 1992), Astérisque, 218, Soc. Math. France, 1993, 9–34
55.	Victor Batyrev, “The cone of effective divisors of threefolds”, Proceedings of the International Conference on Algebra, Part 3 (Novosibirsk, 1989), Contemp. Math., 131, Amer. Math. Soc., Providence, RI, 1992, 337–352
56.	Victor Batyrev, “On the classification of smooth projective toric varieties”, The Tohoku Mathematical Journal. Second Series, 43:4 (1991), 569–585
57.	V. V. Batyrev, D. A. Melnkiov, “A theorem on nonextendability of toric varieties”, Moscow Univ. Math. Bull., 41:3 (1986), 23–27 (to appear)

Presentations in Math-Net.Ru

1.	Глобальное сглаживание минимальных гиперповерхностей Калаби–Яу в $4$-мерных торических многообразиях V. V. Batyrev Memorial conference dedicated to the memory of A. N. Parshin November 12, 2024 11:30
2.	Towards birational classification of 3-folds determined by 4-dimensional empty lattice simplices Victor Batyrev Conference “Birational geometry and Fano varieties” dedicated to Yu.G. Prokhorov 60th anniversary March 13, 2024 17:30
3.	О структурах Ходжа $CM$-типа, связанных с целочисленными симплексами V. V. Batyrev Conference on algebra, algebraic geometry, and number theory on the occasion of academician Igor Rostislavovich Shafarevich 100th birthday June 6, 2023 11:00
4.	The Mori program for non-degenerate toric hypersurfaces of arbitrary dimension V. V. Batyrev Iskovskikh Seminar March 9, 2023 16:45
5.	Целочисленные многогранники и высотные функции на рациональных точках алгебраических торов V. V. Batyrev One-Day Conference Dedicated to the Memory of V. A. Iskovskikh December 27, 2022 11:00
6.	Minimal models of non-degenerate toric hypersurfaces V. V. Batyrev Algebra and geometry: conference on the occasion of V.S. Kulikov 70th birthday May 24, 2022 15:30
7.	Variations on the theme of classical discriminant V. V. Batyrev Multidimensional Residues and Tropical Geometry June 16, 2021 12:00
8.	Stringy Euler numbers of toric Calabi-Yau hypersurfaces Victor Batyrev Iskovskikh Seminar May 28, 2020 18:00
9.	Minimal models of surfaces with $p_g = 1; q = 0$ associated with canonical Fano $3$-polytopes Victor Batyrev "Birational Geometry and Fano varieties" dedicated to V. Iskovskikh June 25, 2019 10:00
10.	Reflective polyhedra. The fourth lecture of mini-course "Combinatorial Mirror Symmetry" V. V. Batyrev Automorphic forms and their applications October 2, 2017 18:00
11.	Toric varieties. The first lecture of mini-course "Combinatorial Mirror Symmetry" V. V. Batyrev Automorphic forms and their applications September 25, 2017 18:00
12.	On virtual Poincaré polynomials of spherical varieties V. V. Batyrev Lie groups and invariant theory March 22, 2017 16:45
13.	Motivic integration on toric varieties and applications V. Batyrev International conference on algebraic geometry, complex analysis and computer algebra August 7, 2016 09:40
14.	The orbit space for the action of a maximal compact subgroup on a homogeneous complex spherical space V. V. Batyrev Lie groups and invariant theory March 9, 2016 16:45
15.	Неархимедовое интегрирование на алгебраических многообразиях и его приложения в бирациональной геометрии V. V. Batyrev Shafarevich Seminar December 22, 2015 15:00
16.	On a combinatorial classification of minimal quasi-homogeneous 3-folds with a $SL(2)\times G_m$-action V. V. Batyrev International conference "Geometry of Algebraic Varieties" dedicated to the memory of V. A. Iskovskikh October 22, 2013 12:15
17.	Mavlyutov's mirror construction and string polytopes of homogeneous spaces V. Batyrev Weekly seminar of Laboratory of algebraic geometry February 15, 2013 17:00
18.	Квазиоднородные $\mathrm{SL}(2)$-многообразия с действием одномерного тора V. Batyrev Lie groups and invariant theory September 23, 2009

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