# Publications

Publications

[1] "An analogue of Torelli's theorem for Kummer surfaces of Jacobians," Math. USSR Izv. 8 (1974), 21--41.

[2] "On Kummer surfaces, " Math. USSR Izv. 9 (1975), 261--275.

[3] "Finite automorphism groups of K\"ahlerian surfaces of type K3," Uspehi matematicheskih nauk 2 (1975), 223--224. (in Russian.)

[4] "Finite automorphism groups of K\"ahlerian surfaces of type K3," Trans. Moscow Math. Soc. 38 (1980), No 2, 71--135.

[5] (with I.V. Dolgachev) "Exceptional singularities of V.I. Arnol'd and K3-surfaces." 7th All-Soviet Union Topol. Conf. Minsk (1977). Thesises of reports. Math. Institute AN BSSR, Minsk 1977.

[6] "Integral symmetric bilinear forms and some of their geometric applications," Math. USSR Izv. 14 (1980), 103--167.

[7] "On factor groups of the automorphism groups of hyperbolic forms modulo subgroups generated by 2-reflections," Soviet Math. Dokl. 20 (1979), 1156--1158.

[8] "On quotient groups of the automorphism groups of hyperbolic forms by the subgroups generated by 2-reflections. Algebraic-geometric applications," J. Soviet Math.22 (1983), 1401--1476.

[9] "On arithmetic groups generated by reflections in Lobachevsky spaces," Math. USSR Izv. 16 (1981),573--601.

[10] "On classification of arithmetic groups generated by reflections in Lobachevsky spaces," Math. USSR Izv. 18 (1982),99--123.

[11] "Involutions of integral quadratic forms and their applications to real algebraic geometry," Math. USSR Izv. 22 (1984), 99--172.

[12] "On a description of the automorphism groups of Enriques surfaces," Soviet Math. Dokl. 30 (1984), 282--285.

[13] "Surfaces of type K3 with finite automorphism group and Picard group of rank three,"

Proc. Steklov. Inst. of Math. 3 (1985), 131--157.

[14] "Local invariants of 4-dimensional pseudo-Riemannian manifolds with Lorentz metric," Problems of geometry, VINITI 17 (1985), pp.87--130. (in Russian.)

[15] "Filtrations of 2-elementary forms and involutions of integral symmetric and skew symmetric bilinear forms," Math. USSR Izv. 49 (1986), 159--182.

[16] "Discrete reflection groups in Lobachevsky spaces and algebraic surfaces,'' Proceedings of the International Congress of Mathematicians Berkeley, California, USA, 1986, 654--671.

[17] (With I.R. Shafarevich) "Geometries and Groups" Universitext, Springer Verlag, 1987, 250 pages.

[18] "On correspondences between surfaces of K3 type," USSR Izv. 30 (1988), 375--383.

[19] (with V.A.Alekseev) "Classification of del Pezzo surfaces with log-terminal singularities of index $\le 2$, involutions of K3 surfaces and reflection groups in Lobachevsky spaces,'' Doklady po matematike i prilogeniyam, MIAN, 2 (1988), 5--151. (in Russian.)

[20] (with V.A.Alekseev) "Classification of del Pezzo surfaces with log-terminal singularities of index $\le 2$ , and involutions on K3 surfaces," Soviet Math. Dokl. 39 (1989), 507--511.

[21] "Del Pezzo surfaces with log-terminal singularities. II," Math. USSR Izv. 33 (1989), 355--372.

[22] "Algebraic surfaces with log-terminal singularities and nef anticanonical class and reflection groups in Lobachevsky spaces," Preprint Max-Planck-Institut f\"ur Mathematik Bonn, MPI/89---28 (1989), 100 pp.

[23] "Del Pezzo surfaces with log-terminal singularities," Math. USSR Sb. 66 (1990), 231--248.

[24] "Del Pezzo surfaces with log-terminal singularities. III," Math. USSR Izv. 35 (1990), 657--675.

[25] "Algebraic 3-folds and the diagram method," Math USSR Izv. 37 (1991), 157--189.

[26] "The remark on arithmetic groups generated by reflections in Lobachevsky spaces," Preprint Max-Planck-Institut f\"ur Mathematik Bonn. MPI/91 (1991).

[27] "On rational maps between K3 surfaces," In Constantin Carath\'eodory: an international tribute, Vol. I, II, p. 946-995, World Sci. Publishing, Teaneck, NJ 1991.

[28] "Weil linear systems on singular K3 surfaces,'' Algebraic geometry and analytic geometry (Tokyo, 1990), 138--164, ICM-90 Satell. Conf. Proc., Springer, Tokyo, 1991.

[29] (with R. Sujatha) "On Brauer groups of real Enriques surfaces", J. reine angew. Math. 444 (1993), 115--154.

[30] "On the Brauer group of real algebraic surfaces", Algebraic Geometry and its applications, Aspects of Mathematics, Vieweg Publ. E; Vol. 25 (1994), 113--136.

[31] "On the Picard number of Fano 3-folds with terminal singularities", J. Math. Kyoto Univ., 34 (1994), no 3, 495--529.

[32] "A lecture on the Kac--Moody Lie algebras of the arithmetic type", Preprint 1994--16 of Queen's University at Kingston, 1994. (see also Duke e-prints, alg-geom/9412003).

[33] (with V.A. Gritsenko) "Siegel automorphic form correction of a Lorentzian Kac--Moody algebra" C. R. Acad. Sci. Paris S\'er. A--B. 321 (1995), 1151--1156.

[34] "On the topological classification of real Enriques surfaces", Amer. Math. Soc. Transl., 173 (1996), no 2, 187--201.

[35] "Basis of the diagram method for generalized reflection groups in Lobachevsky spaces and algebraic surfaces with nef anticanonical class", Intern. J. Mathem. 7 (1996), no 1, 71--108.

[36] "Diagram method for 3-folds and its application to K\"ahler cone and Picard number of Calabi-Yau 3-folds. I." Higher dimensional complex varieties: Proc. of Intern. Confer. held in Trento, Italy, June 15-24, 1994. (eds. M. Andreatta, Th. Peternell) de Gruyter, 1996, 261--328.

[37] "Reflection groups in Lobachevsky spaces and denominator identity for Lorentzian Kac--Moody algebras." Izv. AN Russia. Ser. Mat. 60 (1996), no. 2, 73--106 (see also Duke e-prints, alg-geom/9503003).

[38] (with V.A. Gritsenko) "K3 surfaces, Lorentzian Kac--Moody algebras and mirror symmetry." Math. Res. Let. 3 (1996), no. 2, 211--229. (see also Duke e-prints alg-geom/9510008).

[39] "The remark on discriminants of K3 surfaces moduli as sets of zeros of automorphic forms." , J. of Mathematical Sciences, V. 81, no 3, September 1996 (volume dedicated to Yu.I. Manin), pp. 2738--2743 (Plenum Press). (see also Duke e-prints, alg-geom/9512018).

[40] (with V.A. Gritsenko) "Igusa modular forms and "the simplest" Lorentzian Kac--Moody algebras." Sbornik: Mathematics 187 (1996), no 11, 1601--1641. (see also Duke e-prints, alg-geom/9603010).

[41] (with V.A. Gritsenko) "Siegel automorphic form corrections of some Lorentzi\-an Kac--Moody Lie algebras.", Amer. J. Math., 119 (1997), no 1, 181--224. (see also Duke e-prints, alg-geom/9504006)

[42] (with V.A. Gritsenko) "Automorphic forms and Lorentzian Kac--Moody algebras. Part I." Int. J. Math. 9 (1998), no 2, 153--199. (see also Duke e-prints, alg-geom/9610022).

[43] (with V.A. Gritsenko) "Automorphic forms and Lorentzian Kac--Moody algebras. Part II." Int. J. Math. 9 (1998), no 2, 201--275. (see also Duke e-prints, alg-geom/9611028).

[44] "K3 surfaces with interesting groups of automorphisms". J. Math. Sci. New York, 95 (1999), no 1, 2028-2048 (see also Duke e-prints, alg-geom/9701011)

[45] "A theory of Lorentzian Kac--Moody algebras", Trudy Mezhdunar. konf., posvyashch. 90-letiyu so dnya rozhdeniya L.S. Pontryagina, T. 8: Algebra (Proc. Int. Conf. Devoted to the 90-th Anniversary of L.S. Pontryagin, Vol. 8: Algebra), Moscow: VINITI, 1999, 148-167 (Itogi nauki i tekhniki. Sovremennaya matematika i ee prilozheniya. Tematicheskie obzory, vol. 69). (see also E-prints, math.AG/ 9810001). TeX File (48K).

[46] (with V.A. Gritsenko) "The arithmetic mirror symmetry and Calabi--Yau manifolds." Commun. Math. Phys. 210 (2000), 1-11. (see also Duke e-prints, alg-geom/9612002).

[47] "A remark on algebraic surfaces with polyhedral Mori cone", Nagoya Math. J. 157 (2000), 73-92. (see also e-prints, math.AG/9806047). TeX File (60K).

[48] "On the classification of hyperbolic root systems of rank three." Proc. Steklov Institute of Mathematics, V. 230 (2000), 241 pages. (see also alg-geom/9711032; alg-geom/9712033; math.AG/9905150). TeX File (780K).

[49] (with V.A. Gritsenko) "On classification of Lorentzian Kac-Moody algebras." Russian Math. Surveys 57 (2002), no. 5, 921-979. (see also math.QA/0201162).

[50] (with Carlo Madonna) "On a classical correspondence between K3 surfaces." Proc. Steklov Math. Institute V. 241 (2003), 120-153. (see also math.AG/0206158).

[51] (with Carlo Madonna) "On a classical correspondence between K3 surfaces. II." Strings and geometry, 285-300, Clay Math. Proc., V. 3, Amer. Math. Soc., Providence, RI, 2004. (see also math.AG/0304415).

[52] "On algebraic varieties with finite polyhedral Mori cone." The Fano Conference, 573-589, Univ. Torino, Turin, 2004. (see also math.AG/0305040).

[53] "On correspondences of a K3 surface with itself. I." Proc. Steklov Math. Institute V. 246 (2004), 204-226. (see also arXiv:math/0307355).

[54] "On correspondences of a K3 surface with itself. II."

In Algebraic Geometry, Korea-Japan Conf. in honor of Dolgachev,

July 5-9, 2004, Keum and Kondo editors, Contemporary Mathematics,

V. 422, 2007, Amer. Math. Soc., pages 121-172.

(see also arXiv:math/0309348).

[55] (with Sachiko Saito) "Real K3 surfaces with non-symplectic involution and

applications." Proc. London Math. Soc. (3) 90 (2005),

591-654. (see also arXiv:math.AG/0312396).

[56] (with Valery Alexeev) "Del Pezzo and K3 Surfaces." Mathematical Society of

Japan Memoirs (MSJ Memoirs), Vol. 15 (2006), xvi+149 pages.

(see also arXiv:math.AG/0406536)

[57] "On connected components of moduli of real polarized K3 surfaces."

Izvestiya: Mathematics 72 (2008), no. 1, 91-111. (see also arXiv:math/0507197)

[58] (with Sachiko Saito) "Real K3 surfaces with non-symplectic involution and

applications. II." Proc. London Math. Soc. (3) 95 (2007), no. 1, 20-48. (see also arXiv:math/0508478)

[59] (with Carlo Madonna) "Explicit correspondences of a K3 surface with itself." Izvestiya: Mathematics 72 (2008), no. 3. (see also arXiv:math/0605362, 0606239, 0606289)

[60] "Correspondences of a K3 surface with itself via moduli of sheaves. I." Algebra, Arithmetic, and Geometry (in honor of Yu.I. Manin), Vol. II, Progress in Mathematics 270, (2009), 439 - 464. (see also arXiv:math/0609233).

[61] "Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces." Izvestiya: Mathematics 71 (2007), no. 1, pages 53-56. (see also arXiv:math/0609256).

[62] "On ground fields of arithmetic hyperbolic reflection groups." In Groups and Symmetries, J. Harnad and

P. Winternitz (eds.), CRM Proceedings and Lecture Notes, Vol. 47 (2009), 299-326. (see also arXiv:math/0708.3991)

[63] "On ground fields of arithemtic hyperbolic reflection groups. II." Moscow Math. J. 8 (2008), no. 4, 789-812.

(see also arXiv:math/0710.0162)

[64] "On ground fields of arithmetic hyperbolic reflection groups. III." J. London Math. Soc. (2) 79 (2009), no. 3,

738-756. (see also arXiv:math/0710.2340)

[65] "Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection

group." Proc. Steklov Mathematical Institute, Vol. 273, 2011, 247-256. (see also arXiv:math/0810.2945)

[66] "The transition constant for arithmetic hyperbolic reflection groups." Izvestia: Mathematics 75:5,

2011, 971-1005. (see also arXiv:math/0910.5217)

[67] "Elliptic fibrations on K3 surfaces." Preprint 2012, 21 pages. arXiv:math/1010.3904v4 .

http://xxx.lanl.gov/abs/1010.3904

[68] "Kahlerian K3 surfaces and Niemeier lattices." Preprint 2013, 88 pages. arXiv:math/1109.2879v7 .

http://xxx.lanl.gov/abs/1109.2879

[69] "Kahlerian K3 surfaces and Niemeier lattices.I." Izvestiya: Mathematics 77:5, 2013, 954-997. (see also arXiv:math/1109.2879)

[70] "Elliptic fibrations on K3 surfaces." Proc. of the Edinburgh Math. Soc. Vol. 57, 2014, 253-267. (see also arXiv:math/1010.3904)

[71] "Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups." Izvestiya: Mathematics 79:4, 2015, 740-794.

(see also arXiv:math/1403.6061)

[72] "Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, II." Izvestiya: Mathematics 80:2, 2016,

81--124 (see also arXiv:math/1504:00326).

http://xxx.lanl.gov/abs/1504.00326

[73] (with V.A. Gritsenko) "Lorentzian Kac--Moody algebras with Weyl groups of 2-reflections." Preprint 2016, 73 pages. arXiv:1602.08359v2. http://xxx.lanl.gov/abs/1602.08359

[74] "Kahlerian K3 surfaces and Niemeier lattices, II." Advanced Studies in Pure Mathematics 69, 2016, Development of Moduli Theory -- Kyoto 2013

pp. 421 -- 471. (see also arXiv:math/1109.2879v7).

[75] "Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups. III." Preprint 2016, 49 pages. arXiv: 1608.04373v1. http://xxx.lanl.gov/abs/1608.04373

[76] (with V.A. Gritsenko) "Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac--Moody algebras." Preprint 2017, 15 pages. arXiv:1702.07551v1. http://xxx.lanl.gov/abs/1702.07551

[77] "Classification of Picard lattices of K3 surfaces." Preprint 2017. 68 pages. arXiv:1707.05677v2.

http://xxx.lanl.gov/abs/1707.05677

[78] (with V.A. Gritsenko) "Lorentzian Kac--Moody algebras with Weyl groups of 2-reflections." Proc. London Mathematical Society 116 (2018), issue 3, 485--533 (see also arXiv:1602.08359).

[79] "Classification of degenerations and Picard lattices of Kahlerian K3 surfaces with small finite symplectic automorphism groups. " Preprint 2018, 39 pages, arXiv:1804.00991. http://xxx.lanl.gov/abs/1804.00991