Персоналии: Батырев Виктор Вадимович, Список публикаций

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Батырев Виктор Вадимович

Публикации

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2025
1.	В. В. Батырев, “О классификации гладких торических поверхностей, имеющих ровно одну исключительную кривую”, Бирациональная геометрия и многообразия Фано, Сборник статей. К 60-летию члена-корреспондента РАН Юрия Геннадьевича Прохорова, Труды МИАН, 329, МИАН, М., 2025, 40–55 ; V. V. Batyrev, “On the Classification of Smooth Toric Surfaces with Exactly One Exceptional Curve”, Proc. Steklov Inst. Math., 329 (2025), 33–47

2019
2.	В. В. Батырев, К. Шаллер, “Струнные $E$-функции канонических торических трехмерных многообразий Фано и их приложения”, Изв. РАН. Сер. матем., 83:4 (2019), 26–49 ; V. V. Batyrev, K. Schaller, “Stringy $E$-functions of canonical toric Fano threefolds and their applications”, Izv. Math., 83:4 (2019), 676–697	1 ^[x]

2017
3.	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
4.	V. Batyrev, K. Schaller, “Stringy Chern classes of singular toric varieties and their applications”, Commun.Num.Theor.Phys., 11 (2017), 1–40	5 ^[x]
5.	V. Batyrev, G. Gagliardi, “On the algebraic stringy Euler number”, Proc. Amer. Math. Soc., 145 (2017), 1–13 (to appear)

2016
6.	V. Batyrev, A. Moreau, Satellites of spherical subgroups, 2016 (Published online), 39 pp., arXiv: 1610.07377

2013
7.	V. Batyrev, A. Moreau, “The arc space of horospherical varieties and motivic integration”, Compositio Mathematica, 149:8 (2013), 1327–1352	10 ^[x]
8.	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
9.	V. Batyrev, J. Hofscheier, Lattice polytopes, finite abelian subgroups in $\operatorname{SL}(n)$ and coding theory, 2013 (Published online), 18 pp., arXiv: 1309.5312

2012
10.	K. Altmann, V. Batyrev, Y. Karshon, “Toric geometry. Abstracts from the workshop held April 15–21, 2012.”, Oberwolfach Reports, 9:2 (2012), 1231–1306

2011
11.	V. Batyrev, M. Blume, “On generalisations of Losev-Manin moduli spaces for classical root systems”, Pure Appl. Math. Q., 7:4 (2011), 1053–1084	10 ^[x]
12.	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	15 ^[x]

2010
13.	Victor Batyrev, Dorothee Juny, “Classification of Gorenstein toric Del Pezzo varieties in arbitrary dimension”, Mosc. Math. J., 10:2 (2010), 285–316	13 ^[x]
14.	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	23 ^[x]
15.	V. Batyrev, J. Hofscheier, A generalization of a theorem of G. K. White, 2010 (Published online), 12 pp., arXiv: 1004.3411

2009
16.	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

2008
17.	V. Batyrev, F. Haddad, “On the Geometry of $\operatorname{SL}(2)$-Equivariant Flips”, Mosc. Math. J., 8:4 (2008), 621–646	8 ^[x]
18.	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	32 ^[x]

2007
19.	V. Batyrev, B. Nill, “Multiples of lattice polytopes without interior lattice points”, Mosc. Math. J., 7:2 (2007), 195–207	38 ^[x]

2006
20.	Victor Batyrev, “Lattice polytopes with a given $h^*$-polynomial”, Algebraic and geometric combinatorics, 423, Amer. Math. Soc., Providence, RI, 2006, 1–10 (to appear)
21.	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]
22.	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	2 ^[x]

2004
23.	Victor Batyrev, “Toric degenerations of Fano varieties and constructing mirror manifolds”, The Fano Conference, Univ. Torino, Turin, 2004, 109–122
24.	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	34 ^[x]

2003
25.	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

2002
26.	V. V. Batyrev, E. N. Materov, “Toric residues and mirror symmetry”, Mosc. Math. J., 2:3 (2002), 435–475	16 ^[x]

2001
27.	В. В. Батырев, Ю. Чинкель, “Высотные дзета-функции торических многообразий”, Алгебраическая геометрия – 5, Итоги науки и техн. Сер. Соврем. мат. и ее прил. Темат. обз., 34, ВИНИТИ, М., 2001, 164–194 ; V. V. Batyrev, Yu. Tschinkel, “Height zeta functions of toric varieties”, J. Math. Sci., 82:1 (1996), 3220–3239	29 ^[x]

2000
28.	Victor Batyrev, “Stringy Hodge numbers and Virasoro algebra”, Mathematical Research Letters, 7:2-3 (2000), 155–164
29.	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	73 ^[x]
30.	Victor Batyrev, Canonical abelianization of finite group actions, 2000 (Published online), 4 pp., arXiv: math/0009043

1999
31.	V. Batyrev, E. Selivanova, “Einstein-Kähler metrics on symmetric toric Fano manifolds”, J. Reine Angew. Math., 512 (1999), 225–236	26 ^[x]
32.	Victor Batyrev, “Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs”, Journal of the European Mathematical Society, 1:1 (1999), 5–33	62 ^[x]
33.	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

1998
34.	Victor Batyrev, “Mirror symmetry and toric geometry”, Documenta Mathematica, 1998, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 239–248
35.	V. Batyrev, Ju. Tschinkel, “Manin's conjecture for toric varieties”, Journal of Algebraic Geometry, 7:1 (1998), 15–53
36.	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
37.	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	65 ^[x]
38.	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

1997
39.	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

1996
40.	V. Batyrev, Yu. Tschinkel, “Rational points on some Fano cubic bundles”, C. R. Acad. Sci. Paris Sér. I Math., 323:1 (1996), 41–46
41.	V. Batyrev, D. Dais, “Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry”, Topology, 35:4 (1996), 901–929	79 ^[x]
42.	V. Batyrev, L. Borisov, “Mirror duality and string-theoretic Hodge numbers”, Invent. Math., 126:1 (1996), 183–203	65 ^[x]
43.	V. Batyrev, L. Borisov, “On Calabi-Yau complete intersections in toric varieties”, Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, 39–65
44.	V. Batyrev, Yu. Tschinkel, “Height zeta functions of toric varieties”, Journal of Mathematical Sciences, 82:1 (1996), 3220–3239	29 ^[x]

1995
45.	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	78 ^[x]
46.	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
47.	V. Batyrev, Yu. Tschinkel, “Rational points of bounded height on compactifications of anisotropic tori”, Internat. Math. Res. Notices, 1995, no. 12, 591–635	36 ^[x]

1994
48.	Victor Batyrev, “Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties”, Journal of Algebraic Geometry, 3:3 (1994), 493–535
49.	V. Batyrev, D. Cox, “On the Hodge structure of projective hypersurfaces in toric varieties”, Duke Math. J., 75:2 (1994), 293–338	103 ^[x]

1993
50.	Victor Batyrev, “Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori”, Duke Math. J., 169 (1993), 349–409
51.	Victor Batyrev, “Quantum cohomology rings of toric manifolds”, Journées de Géométrie Algébrique d'Orsay (Orsay, 1992), Astérisque, 218, Soc. Math. France, 1993, 9–34

1992
52.	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

1991
53.	Victor Batyrev, “On the classification of smooth projective toric varieties”, The Tohoku Mathematical Journal. Second Series, 43:4 (1991), 569–585

1990
54.	V. Batyrev, Ju. Manin, “Sur le nombre des points rationnels de hauteur borné des variétés algébriques”, Math. Ann., 286:1-3 (1990), 27–43	112 ^[x]

1986
55.	Батырев В.В., Мельников Д.А., “Теорема о непродолжимости торических многообразий”, Вестник Московского Университета, серия мат. и мех., 1986, № 3, 20–24

1985
56.	В. В. Батырев, “О некоторых численных характеристиках многомерных многообразий Фано”, Изв. АН СССР. Сер. матем., 49:2 (1985), 445–459 ; V. V. Batyrev, “On some numerical characteristics of multidimensional Fano varieties”, Math. USSR-Izv., 26:2 (1986), 423–435	1 ^[x]

1982
57.	Батырев В.В., “Ограниченность степени многомерных торических многообразий Фано”, Вестник Московского Университета, серия мат. и мех., 1982, № 1, 22–27	2 ^[x]

1981
58.	В. В. Батырев, “Трехмерные торические многообразия Фано”, Изв. АН СССР. Сер. матем., 45:4 (1981), 704–717 ; V. V. Batyrev, “Toroidal Fano 3-folds”, Math. USSR-Izv., 19:1 (1982), 13–25	38 ^[x]