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Tr. Mosk. Mat. Obs., 2017, Volume 78, Issue 1, Pages 89–100 (Mi mmo590)  

This article is cited in 1 scientific paper (total in 1 paper)

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

Valery Gritsenkoab, Viacheslav V. Nikulincd

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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.641.31.0001
The first author was supported by Laboratory of Mirror Symmetry NRU HSE, RF government grant, ag. N 14.641.31.0001.


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English version:
Transactions of the Moscow Mathematical Society, 2017, 78, 75–83

Document Type: Article
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

Citation: Valery Gritsenko, Viacheslav V. Nikulin, “Examples of lattice-polarized $K3$ surfaces with automorphic discriminant, and Lorentzian Kac–Moody algebras”, Tr. Mosk. Mat. Obs., 78, no. 1, MCCME, M., 2017, 89–100; Trans. Moscow Math. Soc., 78 (2017), 75–83

Citation in format AMSBIB
\Bibitem{GriNik17}
\by Valery~Gritsenko, Viacheslav~V.~Nikulin
\paper Examples of lattice-polarized $K3$ surfaces with automorphic discriminant, and Lorentzian Kac--Moody algebras
\serial Tr. Mosk. Mat. Obs.
\yr 2017
\vol 78
\issue 1
\pages 89--100
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo590}
\elib{http://elibrary.ru/item.asp?id=37045054}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2017
\vol 78
\pages 75--83
\crossref{https://doi.org/10.1090/mosc/265}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85037661880}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Gritsenko, “Reflective modular forms and applications”, Russian Math. Surveys, 73:5 (2018), 797–864  mathnet  crossref  crossref  adsnasa  isi  elib
  • Trudy Moskovskogo Matematicheskogo Obshchestva
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