Birational geometry of higher-dimensional algebraic varieties.
Biography
Graduated from Lomonosov Moscow State University (Department of Mathematics and Mechanics, Chair of Algebra) in 1984. Ph.D. (Cand. Sci.) — 1987 from Moscow State University. D.Sci. (Mathematics) — 1998 from Steklov Institute of Mathematics. The lists of my publications contains about 80 items. In 1998 I was an invited speaker at the International Congress of Mathematicians in Berlin (45-minute sectional address).
Main publications:
A. Pukhlikov, Birationally Rigid Varieties, Mathematical Surveys and Monographs, 190, Amer. Math. Soc., Providence, RI, 2013 , 367 pp.
A. V. Pukhlikov, “Birationally rigid Fano fibrations”, Izv. Math., 64:3 (2000), 563–581
A. V. Pukhlikov, “Birationally rigid Fano double hypersurfaces”, Sb. Math., 191:6 (2000), 883–908
A. V. Pukhlikov, “Birational automorphisms of Fano hypersurfaces”, Invent. Math., 134:2 (1998), 401–426
A. V. Pukhlikov, “Birational automorphisms of algebraic threefolds with a pencil of Del Pezzo surfaces”, Izv. Math., 62:1 (1998), 115–155
A. V. Pukhlikov, “Affine complements in the projective space with the trivial group of automorphisms”, Trudy Mat. Inst. Steklova, 328, 2025 (to appear)
2024
2.
A. V. Pukhlikov, “Birationally rigid hypersurfaces with quadratic singularities of low rank”, Sb. Math., 215:6 (2024), 823–840
2022
3.
A. V. Pukhlikov, “Birational geometry of varieties fibred into complete intersections of codimension two”, Izv. Math., 86:2 (2022), 334–411
4.
A. V. Pukhlikov, “Effective results in the theory of birational rigidity”, Russian Math. Surveys, 77:2 (2022), 301–354
2021
5.
A. V. Pukhlikov, “Birational geometry of singular Fano double spaces of index two”, Sb. Math., 212:4 (2021), 551–566
6.
A. V. Pukhlikov, “Remarks on Galois Rational Coverings”, Math. Notes, 110:2 (2021), 242–247
2019
7.
D. Evans, A. V. Pukhlikov, “Birationally rigid complete intersections of high codimension”, Izv. Math., 83:4 (2019), 743–769
8.
A. V. Pukhlikov, “Birationally Rigid Finite Covers of the Projective Space”, Proc. Steklov Inst. Math., 307 (2019), 232–244
2018
9.
A. V. Pukhlikov, “Automorphisms of certain affine complements in projective space”, Sb. Math., 209:2 (2018), 276–289
10.
Aleksandr V. Pukhlikov, “Canonical and log canonical thresholds of Fano complete intersections”, Eur. J. Math., 4:1 (2018), 381–398
Aleksandr V. Pukhlikov, “The Gabrielov-Khovanskii problem for polynomials”, Arnold Math. J., 2:1 (2016), 29–68
2015
18.
A. V. Pukhlikov, “Two Inequalities for a Sequence of Blow-Ups”, Math. Notes, 97:6 (2015), 970–973
19.
A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837
2014
20.
Th. Eckl, A. Pukhlikov, “On the locus of nonrigid hypersurfaces”, Automorphisms in Birational and Affine Geometry (Levico Terme, Italy, October 2012), Springer Proceedings in Mathematics & Statistics, 79, Springer, 2014, 121–139
A. V. Pukhlikov, “Birational rigidity of Fano complete intersections”, Dokl. Math., 87:1 (2013), 34–35
2012
26.
A. V. Pukhlikov, “$K$-Trivial Structures on Fano Complete Intersections”, Math. Notes, 91:4 (2012), 568–574
27.
A. V. Pukhlikov, “On the multiplicity of solutions of a system of algebraic equations”, Proc. Steklov Inst. Math., 276 (2012), 234–249
2010
28.
A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. Math., 74:5 (2010), 925–991
29.
A. V. Pukhlikov, “Existence of the Kähler–Einstein Metric on Certain Fano Complete Intersections”, Math. Notes, 88:4 (2010), 552–558
30.
A. V. Pukhlikov, “Birationally rigid varieties. II. Fano fibre spaces”, Russian Math. Surveys, 65:6 (2010), 1083–1171
2009
31.
A. V. Pukhlikov, “Rationality problem and birational rigidity”, Cohomological and geometric approaches to rationality problems, Progr. Math., 282, Birkhäuser, Boston, 2009, 275–311
32.
A. V. Pukhlikov, “Birational geometry of algebraic varieties with a pencil of Fano cyclic covers”, Pure Appl. Math. Q., 5:2, Special Issue: In honor of Friedrich Herzebruch (2009), 641–700
A. V. Pukhlikov, “Singularities of Algebraic Subvarieties and Problems of Birational Geometry”, Proc. Steklov Inst. Math., 267 (2009), 235–247
34.
A. V. Pukhlikov, “Birational Geometry of Singular Fano Varieties”, Proc. Steklov Inst. Math., 264 (2009), 159–177
35.
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
2010
36.
A. V. Pukhlikov, “On the self-intersection of a movable linear system”, J. Math. Sci., 164:1 (2010), 119–130
2008
37.
A. V. Pukhlikov, “Birational geometry of Fano double covers”, Sb. Math., 199:8 (2008), 1225–1250
2007
38.
A. V. Pukhlikov, “Explicit examples of birationally rigid Fano varieties”, Mosc. Math. J., 7:3 (2007), 543–560
A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942
40.
A. V. Pukhlikov, “Kvadratichnye metody v teorii optimalnogo upravleniya i teorii sistem”, Nelineinaya dinamika i upravlenie, 5, Fizmatlit, M., 2007, 69–98
2006
41.
A. V. Pukhlikov, “Birational geometry of algebraic varieties with a pencil of Fano complete intersections”, Manuscripta Math., 121:4 (2006), 491–526
A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. III”, Sb. Math., 197:3 (2006), 335–368
2005
43.
A. V. Pukhlikov, “Geometry of discontinuous systems near a manifold of singularities of third order”, Differ. Equ., 41:12 (2005), 1710–1716
44.
A. V. Pukhlikov, “Biratsionalno zhestkie pryamye proizvedeniya Fano”, Dokl. RAN, 401:2 (2005), 163–165
45.
A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255
2004
46.
A. V. Pukhlikov, “Birationally rigid Fano varieties”, The Fano Conference, Univ. Torino, Turin, 2004, 659–681
47.
A. V. Pukhlikov, “Optimal control of distributions”, Nonlinear dynamics and control. 2, Comput. Math. Model., 15:3 (2004), 223–256
2007
48.
A. V. Pukhlikov, “Integral representations in the theory of controlled systems”, Nonlinear dynamics and control, Comput. Math. Model., 18, no. 4, 2007, 344–368
49.
A. V. Pukhlikov, “Fano direct products as rationally connected fibrations”, J. Math. Sci., 140:2 (2007), 303–320
2004
50.
A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. II”, Sb. Math., 195:11 (2004), 1665–1702
51.
A. V. Pukhlikov, “Birationally rigid varieties with a pencil of double Fano covers. I”, Sb. Math., 195:7 (2004), 1039–1071
2003
52.
A. V. Pukhlikov, “Birationally rigid singular Fano hypersurfaces”, Algebraic geometry, 12, J. Math. Sci. (N. Y.), 115:3 (2003), 2428–2436
A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. Math., 67:3 (2003), 555–596
2002
54.
A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano hypersurfaces”, Dokl. Akad. Nauk, 385:1 (2002), 28–30
55.
A. V. Pukhlikov, “Discontinuous dynamical systems in optimal control theory”, Nonlinear dynamics and control, Comput. Math. Model., 13:1 (2002), 81–105
56.
A. V. Pukhlikov, “Birational Automorphisms of Algebraic Varieties with a Pencil of Fano Double Covers”, Funct. Anal. Appl., 36:1 (2002), 74–75
57.
A. V. Pukhlikov, “Birationally rigid Fano hypersurfaces”, Izv. Math., 66:6 (2002), 1243–1269
58.
A. V. Pukhlikov, “Birational automorphisms of Fano hypersurfaces with singularities”, Russian Math. Surveys, 57:1 (2002), 157–158
59.
F. Campana, Th. Peternell, A. V. Pukhlikov, “Generalized Tsen's theorem and rationally connected Fano fibrations”, Sb. Math., 193:10 (2002), 1443–1468
60.
A. V. Pukhlikov, “Birationally rigid Fano hypersurfaces with isolated singularities”, Sb. Math., 193:3 (2002), 445–471
2001
61.
F. Kampana, T. Peternell, A. V. Pukhlikov, “Obobschennaya teorema Tzena i ratsionalno svyaznye mnogoobraziya”, Dokl. RAN, 381:6 (2001), 742–744
62.
A. V. Pukhlikov, “Birationally rigid Fano complete intersections”, J. Reine Angew. Math., 541 (2001), 55–79
A. V. Pukhlikov, “Singularities in discontinuous dynamical systems”, Dokl. Akad. Nauk, 378:4 (2001), 456–458
64.
A. V. Pukhlikov, “The geometry of discontinuous systems near a hyperbolic singular point of a sliding field”, Differ. Equ., 37:3 (2001), 377–400
1997
65.
A. V. Pukhlikov, “Birational automorphisms of double spaces with singularities”, J. Math. Sci. (New York), 85:4 (1997), 2128–2141
1996
66.
V. A. Iskovskikh, A. V. Pukhlikov, “Birational automorphisms of multidimensional algebraic manifolds”, J. Math. Sci., 82:4 (1996), 3528–3613
2000
67.
A. Corti, A. Pukhlikov, M. Reid, “Fano 3-fold hypersurfaces”, Explicit birational geometry of 3-folds, London Math. Soc. Lecture Note Ser., 281, Cambridge Univ. Press, Cambridge, 2000, 175–258
68.
A. V. Pukhlikov, “Essentials of the method of maximal singularities”, Explicit birational geometry of 3-folds, London Math. Soc. Lecture Note Ser., 281, Cambridge Univ. Press, Cambridge, 2000, 73–100
69.
A. V. Pukhlikov, “Biratsionalnye avtomorfizmy polnykh peresechenii Fano”, Doklady Akademii nauk, 374:2 (2000), 160–163
70.
A. V. Pukhlikov, “A Gauss–Ostrogradskii theorem for integral transforms over the Euler characteristic”, Integral Transform. Spec. Funct., 9:4 (2000), 299–312
A. V. Pukhlikov, “Birationally rigid Fano fibrations”, Izv. Math., 64:3 (2000), 563–581
72.
A. V. Pukhlikov, “Fiber-wise birational correspondences”, Math. Notes, 68:1 (2000), 103–112
73.
A. V. Pukhlikov, “Birational automorphisms of algebraic varieties with a pencil of double quadrics”, Math. Notes, 67:2 (2000), 192–199
74.
A. V. Pukhlikov, “Birationally rigid Fano double hypersurfaces”, Sb. Math., 191:6 (2000), 883–908
1999
75.
A. V. Pukhlikov, “Geometry of discontinuous systems near an elliptic singularity”, Differential Equations, 35:11 (1999), 1516–1529 (2000)
76.
A. V. Pukhlikov, “Structurally stable singularities of discontinuous dynamical systems”, Differential Equations, 35:5 (1999), 675–682
77.
A. V. Pukhlikov, “Certain examples of birationally rigid varieties with a pencil of double quadrics”, Algebraic geometry, 9, J. Math. Sci. (New York), 94:1 (1999), 986–995
A. V. Pukhlikov, “Birational Automorphisms of Fano Double Covers”, Funct. Anal. Appl., 33:4 (1999), 313–314
79.
A. V. Pukhlikov, “Birationally rigid varieties with a sheaf of Fano hypersurfaces”, Russian Math. Surveys, 54:1 (1999), 260–261
80.
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
1998
81.
A. V. Pukhlikov, “Optimal bilinear systems on a plane”, Differential Equations, 34:11 (1998), 1516–1521 (1999)
82.
A. V. Pukhlikov, “Birational automorphisms of three-dimensional algebraic varieties fibered by Del Pezzo surfaces”, Dokl. Akad. Nauk, 361:1 (1998), 14–16
83.
A. V. Pukhlikov, “The discrete maximum principle”, Dokl. Akad. Nauk, 360:6 (1998), 747–749
A. V. Pukhlikov, “Birational automorphisms of higher-dimensional algebraic varieties”, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Doc. Math., Extra Vol. II, 1998, 97–107 (electronic)
86.
A. V. Pukhlikov, “Birational automorphisms of algebraic threefolds with a pencil of Del Pezzo surfaces”, Izv. Math., 62:1 (1998), 115–155
1997
87.
A. V. Pukhlikov, “Integral transformations in the theory of controllable dynamic systems”, Dokl. Math., 55:2 (1997), 315–317
88.
A. V. Pukhlikov, “Integral representations in the theory of discrete controllable systems”, Dokl. Math., 55:2 (1997), 312–314
89.
A. V. Pukhlikov, “Birational automorphisms of algebraic threefolds fibred by cubic surfaces”, Russian Math. Surveys, 52:1 (1997), 230–231
90.
A. V. Pukhlikov, Mat. Pros., 1, MCCME, Moscow, 1997, 85–89
1996
91.
A. V. Pukhlikov, “Fredholm determinants and the Newton method in problems of the control of distributions”, Automat. Remote Control, 57:6 (1996), 814–818
92.
A. V. Pukhlikov, “Singular regimes in problems of the control of distributions. I. Scalar controls”, Automat. Remote Control, 57:5 (1996), 634–643
1995
93.
A. V. Pukhlikov, “Degenerations of Hamiltonian structures in optimal control problems”, Differential Equations, 31:11 (1995), 1841–1847 (1996)
94.
A. V. Pukhlikov, “Analytic representations in problems of the control of distributions”, Automat. Remote Control, 56:12 (1995), 1698–1708 (1996)
95.
A. V. Pukhlikov, “Rational curves with prescribed branches”, Moscow Univ. Math. Bull., 50:1 (1995), 20–22
96.
A. V. Pukhlikov, “Hamiltonian structures in optimal control theory”, J. Dynam. Control Systems, 1:3 (1995), 379–401
A. V. Pukhlikov, “Problems of the control of distributions in dynamical systems”, Automat. Remote Control, 56:4 (1995), 517–525
98.
A. V. Pukhlikov, “A remark on the theorem of V. A. Iskovskikh and Yu. I. Manin on a three-dimensional quartic”, Proc. Steklov Inst. Math., 208 (1995), 244–254
1994
99.
A. V. Pukhlikov, “Liouville's theorem in optimal control problems”, Differential Equations, 30:11 (1994), 1808–1814 (1995)
1993
100.
A. G. Khovanskii, A. V. Pukhlikov, “Integral transforms based on Euler characteristic and their applications”, Integral Transform. Spec. Funct., 1:1 (1993), 19–26
A. V. Pukhlikov, “Poisson's theorem in optimal control problems”, Differential Equations, 29:11 (1993), 1685–1690 (1994)
102.
A. I. Propoĭ, A. V. Pukhlikov, “Quadratic approximation in nonlinear extremal problems”, Phys. Dokl., 38:8 (1993), 320–322 (1994)
103.
V. A. Iskovskih, A. V. Pukhlikov, “Birational automorphisms of Fano varieties”, Geometry of complex projective varieties (Cetraro, 1990), Sem. Conf., 9, Mediterranean, Rende, 1993, 191–201
104.
A. V. Pukhlikov, “Asymptotically periodic systems. II”, Autom. Remote Control, 54:10 (1993), 1493–1503
105.
A. V. Pukhlikov, “Asymptotically periodic systems. I”, Autom. Remote Control, 54:5 (1993), 747–754
106.
A. I. Propoǐ, A. V. Pukhlikov, “The stochastic Newton method in nonlinear extremal problems”, Autom. Remote Control, 54:4 (1993), 605–613
107.
A. V. Pukhlikov, A. G. Khovanskii, “Finitely additive measures of virtual polyhedra”, St. Petersburg Math. J., 4:2 (1993), 337–356
108.
A. V. Pukhlikov, A. G. Khovanskii, “The Riemann–Roch theorem for integrals and sums of quasipolynomials on virtual polytopes”, St. Petersburg Math. J., 4:4 (1993), 789–812
1989
109.
A. V. Pukhlikov, “Maximal singularities on the Fano variety $V_6^3$”, Moscow Univ. Math. Bull., 44:2 (1989), 70–75
110.
A. V. Pukhlikov, “Birational automorphisms of a double space and double quadric”, Math. USSR-Izv., 32:1 (1989), 233–243
111.
A. V. Pukhlikov, “Birational automorphisms of a three-dimensional quartic with a quadratic singularity”, Math. USSR-Sb., 63:2 (1989), 457–482
1987
112.
A. V. Pukhlikov, “Birational isomorphisms of four-dimensional quintics”, Invent. Math., 87:2 (1987), 303–329
Бирационально жесткие расслоения Фано Alexander Pukhlikov Annual memorial conference dedicated to the memory of Andrei Nikolaevich Tyurin October 28, 2014 11:40