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Classification of Degenerations and Picard Lattices of Kählerian K3 Surfaces with Symplectic Automorphism Group C4

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Abstract

In the author’s papers of 2013–2018, the degenerations and Picard lattices of Kählerian K3 surfaces with finite symplectic automorphism groups of high order were classified. For the remaining groups of small order—D6, C4, (C2)2, C3, C2, and C1—the classification was not completed because each of these cases requires very long and difficult considerations and calculations. The case of D6 was recently completely studied in the author’s paper of 2019. In the present paper an analogous complete classification is presented for the cyclic group C4 of order 4.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Viacheslav V. Nikulin

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX, UK

    Viacheslav V. Nikulin

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  1. Viacheslav V. Nikulin
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Correspondence to Viacheslav V. Nikulin.

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In memory of Igor Rostislavovich Shafarevich on the occasion of his 95th birthday

This article was submitted by the author simultaneously in Russian and English

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Vol. 307, pp. 148–179.

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Nikulin, V.V. Classification of Degenerations and Picard Lattices of Kählerian K3 Surfaces with Symplectic Automorphism Group C4. Proc. Steklov Inst. Math. 307, 130–161 (2019). https://doi.org/10.1134/S0081543819060087

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  • DOI: https://doi.org/10.1134/S0081543819060087

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