Valery Gritsenko, Viacheslav V. Nikulin, “Examples of lattice-polarized <nobr>$K3$</nobr> surfaces with automorphic discriminant, and Lorentzian Kac–Moody algebras”, Tr. Mosk. Mat. Obs., 2017, Volume 78, Issue 1,Pages <nobr>89

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

Valery Gritsenko^ab, Viacheslav V. Nikulin^cd

^a Laboratoire Paul Painlevé et IUF, Université de Lille 1, France
^b National Research University “Higher School of Economics”, Russian Federation
^c Steklov Mathematical Institute, ul. Gubkina 8, GSP-1, Russia
^d Department of Pure Mathematics, The University of Liverpool, Liverpool L69 3BX, United Kingdom

Abstract: 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.

Key words and phrases: $K3$ surface, Picard lattice, polarization, moduli space, degeneration, discriminant, Lie algebra, Kac–Moody algebra, root system, automorphic form.

UDC: 512.774.3, 512.774.5, 512.818.4, 515.178.1

MSC: 14J15, 14J28, 14J33, 14J60, 14J81

Received: 14.03.2017
Revised: 13.04.2017