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Transactions of the Moscow Mathematical Society

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


Authors: Valery Gritsenko and Viacheslav V. Nikulin
Translated by: the authors
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 78 (2017), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2017, 75-83
MSC (2010): Primary 14J15, 14J28, 14J33, 14J60, 14J81
DOI: https://doi.org/10.1090/mosc/265
Published electronically: December 1, 2017
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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.


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Valery Gritsenko
Affiliation: Laboratoire Paul Painlevé et IUF, Université de Lille 1, France – and – National Research University “Higher School of Economics”, Russian Federation
Email: Valery.Gritsenko@math.univ-lille1.fr

Viacheslav V. Nikulin
Affiliation: Steklov Mathematical Institute, ul. Gubkina 8, Moscow 117966, GSP-1, Russia – and – Department of Pure Mathematics, The University of Liverpool, Liverpool L69 3BX, United Kingdom
Email: nikulin@mi.ras.ru\\ vvnikulin@list.ru\\ vnikulin@liv.ac.uk

DOI: https://doi.org/10.1090/mosc/265
Keywords: K3 surface, Picard lattice, polarization, moduli space, degeneration, discriminant, Lie algebra, Kac--Moody algebra, root system, automorphic form
Published electronically: December 1, 2017
Additional Notes: The first author was supported by Laboratory of Mirror Symmetry NRU HSE, RF government grant, ag. N 14.641.31.0001.
Dedicated: Dedicated to É. B. Vinberg on the occasion of his 80th birthday
Article copyright: © Copyright 2017 American Mathematical Society

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