Classification of degenerations and Picard lattices of Kahlerian K3 surfaces with the symplectic automorphism group (C_2)^2

Autor: Nikulin, Viacheslav V.

Publikováno v: For D6: Izv. RAN: Ser. Mat., 83:6 (2019),133---166 (in Russian); Izv. Math., 83:6 (2019), 1201---1233 (in English). For C4: Proc. MIAN, 307 (2019), 148---179 (in Russian); Proc. Steklov Inst. Math., 307(2019), 130---161 (in English)

Var3: In our papers 2013--2018 we classified degenerations and Picard lattices of Kahlerian K3 surfaces with finite symplectic automorphism groups of high order. For remaining groups of small order: $D_6$, $C_4$, $(C_2)^2$, $C_3$, $C_2$ and $C_1$ it

Externí odkaz: http://arxiv.org/abs/1804.00991

Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac--Moody algebras

Autor: Gritsenko, Valery, Nikulin, Viacheslav V.

Publikováno v: Proc. Moscow Math. Soc. 2017, 78:1, 89-100 (in Russian); Trans. Moscow Math. Soc. 2017, 78, 75-83 (English)

Using our results about Lorentzian Kac--Moody algebras and arithmetic mirror symmetry, we give six series of examples of lattice-polarized K3 surfaces with automorphic discriminant.
Comment: 15 pages

Externí odkaz: http://arxiv.org/abs/1702.07551

Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections

Autor: Gritsenko, Valery, Nikulin, Viacheslav V.

Publikováno v: Proc.London.Math.Soc. 116(2018) 485-533

We describe a new large class of Lorentzian Kac--Moody algebras. For all ranks, we classify 2-reflective hyperbolic lattices S with the group of 2-reflections of finite volume and with a lattice Weyl vector. They define the corresponding hyperbolic K

Externí odkaz: http://arxiv.org/abs/1602.08359

Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups

Autor: Nikulin, Viacheslav V.

Publikováno v: Izv. RAN. Ser. Mat, 2015, 79:4, 103-158 (in Russian); Izvestiya: Mathematics, 2015, 79:4, 740-794 (English)

Using results of our preprint "Kahlerian K3 surfaces and Niemeier lattices" arXiv:1109.2879 (and the corresponding papers), we classify degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups.
Comment: Var5: 71 pages. T

Externí odkaz: http://arxiv.org/abs/1403.6061

Elliptic fibrations on K3 surfaces

Autor: Nikulin, Viacheslav V.

Publikováno v: Proceedings of the Edinburgh Mathematical Society (2014) 57, 253-267

This is mainly a review of my results related to the title. We discuss, how many elliptic fibrations and elliptic fibrations with infinite automorphism group (or the Mordell-Weil group) an algebraic K3 surface over an algebraically closed field can h

Externí odkaz: http://arxiv.org/abs/1010.3904