Persons: Pukhlikov Aleksandr Valentinovich

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Pukhlikov Aleksandr Valentinovich

Statistics Math-Net.Ru
Total publications:	36
Scientific articles:	34
Citations to the author:	301
Cited articles:	24
Citing authors:	31
Presentations:	1

Number of views:
This page:	610
Abstract pages:	2390
Full texts:	580
References:	109

Scientific status:

Senior Researcher

Scientific degree:

Doctor of physico-mathematical sciences (1998)

Speciality:

01.01.06 (Mathematical logic, algebra, and number theory)

Birth date:

18.12.1962

Phone:

+7 (495) 938 37 33

Fax:

+7 (499) 135 05 55

E-mail:

, ,

Keywords:

algebraic variety; Fano variety; Fano fibration; birational map; birational rigidity; divisor; linear system; singularity; intersection theory; optimal control; optimal system; discontinuous Hamiltonian system.

UDC:

512.76, 512.776, 512.724, 517.977, 513.6, 512.7

MSC:

14E05, 14E07, 14E08, 14J45, 14J30, 14M10, 14M20, 14M25, 14D06, 93C10, 37D40

Subject

Birational geometry of higher-dimensional algebraic varieties. The concept of birational rigidity of Fano varieties and Fano fibrations has been introduced and studied. Birational rigidity was proved for the following large classes of higher-dimensional Fano varieties: Fano hypersurfaces $V_M\subset{\Bbb P}^M$, $M\ge 5$, with isolated terminal singularities of general position, smooth Fano double covers of index 1, Fano complete intersections $V_{d_1\cdot\dots\cdot d_k}\subset{\Bbb P}^{M+k}$ with $k

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). Permanent position — Steklov Institute of Mathematics.

Main publications

Pukhlikov A. V. Birational automorphisms of Fano hypersurfaces // Invent. Math. 1998, 134 (2), 401–426.

List of publications on Google Scholar

List of publications on ZentralBlatt

Personal webpage on MathSciNet

Publications in Math-Net.Ru

1.	Бирациональная геометрия двойных пространств Фано индекса два A. V. Pukhlikov Izv. RAN. Ser. Mat., Forthcoming paper
2.	Singularities of Algebraic Subvarieties and Problems of Birational Geometry A. V. Pukhlikov Tr. Mat. Inst. Steklova, 2009, 267, 245–257
3.	Birational Geometry of Singular Fano Varieties A. V. Pukhlikov Tr. Mat. Inst. Steklova, 2009, 264, 165–183
4.	On the self-intersection of a movable linear system A. V. Pukhlikov Fundam. Prikl. Mat., 2008, 14:6, 177–192
5.	Birational geometry of Fano double covers A. V. Pukhlikov Mat. Sb., 2008, 199:8, 123–148
6.	Explicit examples of birationally rigid Fano varieties A. V. Pukhlikov Mosc. Math. J., 2007, 7:3, 543–560
7.	Birationally rigid varieties. I. Fano varieties A. V. Pukhlikov Uspekhi Mat. Nauk, 2007, 62:5(377), 15–106
8.	Birationally rigid varieties with a pencil of Fano double covers. III A. V. Pukhlikov Mat. Sb., 2006, 197:3, 35–68
9.	Birational geometry of Fano direct products A. V. Pukhlikov Izv. RAN. Ser. Mat., 2005, 69:6, 153–186
10.	Fano direct products as rationally connected fibrations A. V. Pukhlikov Fundam. Prikl. Mat., 2004, 10:4, 183–206
11.	Birationally rigid varieties with a pencil of Fano double covers. II A. V. Pukhlikov Mat. Sb., 2004, 195:11, 119–156
12.	Birationally rigid varieties with a pencil of double Fano covers. I A. V. Pukhlikov Mat. Sb., 2004, 195:7, 127–160
13.	Birationally rigid iterated Fano double covers A. V. Pukhlikov Izv. RAN. Ser. Mat., 2003, 67:3, 139–182
14.	Birational Automorphisms of Algebraic Varieties with a Pencil of Fano Double Covers A. V. Pukhlikov Funkts. Anal. Prilozh., 2002, 36:1, 88–90
15.	Birationally rigid Fano hypersurfaces A. V. Pukhlikov Izv. RAN. Ser. Mat., 2002, 66:6, 159–186
16.	Birational automorphisms of Fano hypersurfaces with singularities A. V. Pukhlikov Uspekhi Mat. Nauk, 2002, 57:1(343), 163–164
17.	Generalized Tsen's theorem and rationally connected Fano fibrations F. Campana, Th. Peternell, A. V. Pukhlikov Mat. Sb., 2002, 193:10, 49–74
18.	Birationally rigid Fano hypersurfaces with isolated singularities A. V. Pukhlikov Mat. Sb., 2002, 193:3, 135–160
19.	Birational automorphisms of double spaces with singularities A. V. Pukhlikov Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2001, 24, 177–196
20.	Birational automorphisms of multidimensional algebraic manifolds V. A. Iskovskikh, A. V. Pukhlikov Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2001, 19, 5–139
21.	Birationally rigid Fano fibrations A. V. Pukhlikov Izv. RAN. Ser. Mat., 2000, 64:3, 131–150
22.	Fiber-wise birational correspondences A. V. Pukhlikov Mat. Zametki, 2000, 68:1, 120–130
23.	Birational automorphisms of algebraic varieties with a pencil of double quadrics A. V. Pukhlikov Mat. Zametki, 2000, 67:2, 241–249
24.	Birationally rigid Fano double hypersurfaces A. V. Pukhlikov Mat. Sb., 2000, 191:6, 101–126
25.	Birational Automorphisms of Fano Double Covers A. V. Pukhlikov Funkts. Anal. Prilozh., 1999, 33:4, 88–90
26.	Birationally rigid varieties with a sheaf of Fano hypersurfaces A. V. Pukhlikov Uspekhi Mat. Nauk, 1999, 54:1(325), 261–262
27.	Birational automorphisms of algebraic threefolds with a pencil of Del Pezzo surfaces A. V. Pukhlikov Izv. RAN. Ser. Mat., 1998, 62:1, 123–164
28.	«Вещественное» доказательство основной теоремы алгебры A. V. Pukhlikov Mat. Pros., Series 3, 1997, 1, 85–89
29.	Birational automorphisms of algebraic threefolds fibred by cubic surfaces A. V. Pukhlikov Uspekhi Mat. Nauk, 1997, 52:1(313), 235–236
30.	A remark on the theorem of V. A. Iskovskikh and Yu. I. Manin on a three-dimensional quartic A. V. Pukhlikov Trudy Mat. Inst. Steklov., 1995, 208, 278–289
31.	The Riemann–Roch theorem for integrals and sums of quasipolynomials on virtual polytopes A. V. Pukhlikov, A. G. Khovanskii Algebra i Analiz, 1992, 4:4, 188–216
32.	Finitely additive measures of virtual polyhedra A. V. Pukhlikov, A. G. Khovanskii Algebra i Analiz, 1992, 4:2, 161–185
33.	Birational automorphisms of a double space and double quadric A. V. Pukhlikov Izv. Akad. Nauk SSSR Ser. Mat., 1988, 52:1, 229–239
34.	Birational automorphisms of a three-dimensional quartic with a quadratic singularity A. V. Pukhlikov Mat. Sb. (N.S.), 1988, 135(177):4, 472–496

35.	Vasilii Alekseevich Iskovskikh (obituary) 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 Uspekhi Mat. Nauk, 2009, 64:5(389), 167–174
36.	Vasilii Alekseevich Iskovskikh (on his 60th birthday) 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 Uspekhi Mat. Nauk, 1999, 54:4(328), 183–187

Presentations

Birational geometry of Fano double spaces of index two
International conference "Geometry of Algebraic Varieties" dedicated to the memory of Vasily Alexeevich Iskovskikh
June 29, 2009 16:30

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