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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 4, Pages 115–177 (Mi izv8719)  

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

Classification of Picard lattices of K3 surfaces

V. V. Nikulinab

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

Abstract: Using the results of our papers [1]–[4] on the classification of degenerations of Kählerian K3 surfaces, we classify the Picard lattices of Kählerian K3 surfaces. By classification we mean classification depending on their possible finite symplectic automorphism groups and their non-singular rational curves when the Picard lattice is negative definite.

Keywords: K3 surface, complex surface, Picard lattice, automorphism group, rational curve, degeneration, integer symmetric bilinear form.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/im8719

Full text: PDF file (899 kB)
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English version:
Izvestiya: Mathematics, 2018, 82:4, 752–816

Bibliographic databases:

UDC: 512.774.4+515.173.4+512.722+512.774.2+512.774.3+512.647.2
MSC: 14J28, 14J10, 14C22, 14J50
Received: 15.09.2017

Citation: V. V. Nikulin, “Classification of Picard lattices of K3 surfaces”, Izv. RAN. Ser. Mat., 82:4 (2018), 115–177; Izv. Math., 82:4 (2018), 752–816

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  • https://doi.org/10.4213/im8719
  • http://mi.mathnet.ru/eng/izv/v82/i4/p115

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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. Schaffler L., “K3 Surfaces With Z(2)(2) Symplectic Action”, Rocky Mt. J. Math., 48:7 (2018), 2347–2383  crossref  mathscinet  zmath  isi  scopus
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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