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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 6, Pages 133–166 (Mi izv8868)  

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

Classification of degenerations and Picard lattices of Kählerian K3 surfaces with symplectic automorphism group $D_6$

V. V. Nikulinab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

Abstract: In [1][6] we classified the degenerations and Picard lattices of Kählerian K3 surfaces with finite symplectic automorphism groups of high order. This classification was not considered for the remaining groups of small order ($D_6$, $C_4$, $(C_2)^2$, $C_3$, $C_2$ and $C_1$) because each of these cases requires very long and difficult considerations and calculations.
Here we consider this classification for the dihedral group $D_6$ of order $6$.

Keywords: K3 surface, degeneration, Picard lattice, automorphism group.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation
Supported by the grant for creation and development of the International Mathematical Centre of World Level in MIAN within the framework of the national project “Science”.


DOI: https://doi.org/10.4213/im8868

Full text: PDF file (719 kB)
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English version:
Izvestiya: Mathematics, 2019, 83:6, 1201–1233

Bibliographic databases:

UDC: 512.774.4+515.173.4+512.722+512.774.2+512.774.3+512.647.2
MSC: Primary 14J28; Secondary 14J50, 14J10, 14C22
Received: 11.11.2019

Citation: V. V. Nikulin, “Classification of degenerations and Picard lattices of Kählerian K3 surfaces with symplectic automorphism group $D_6$”, Izv. RAN. Ser. Mat., 83:6 (2019), 133–166; Izv. Math., 83:6 (2019), 1201–1233

Citation in format AMSBIB
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\by V.~V.~Nikulin
\paper Classification of~degenerations and Picard lattices of~K\" ahlerian
K3 surfaces with symplectic automorphism group $D_6$
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\vol 83
\issue 6
\pages 133--166
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\crossref{https://doi.org/10.4213/im8868}
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\transl
\jour Izv. Math.
\yr 2019
\vol 83
\issue 6
\pages 1201--1233
\crossref{https://doi.org/10.1070/IM8868}
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  • https://doi.org/10.4213/im8868
  • http://mi.mathnet.ru/eng/izv/v83/i6/p133

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Viacheslav V. Nikulin, “Classification of Degenerations and Picard Lattices of Kählerian K3 Surfaces with Symplectic Automorphism Group $C_4$”, Proc. Steklov Inst. Math., 307 (2019), 130–161  mathnet  crossref  crossref  isi  elib
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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