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Tr. Mat. Inst. Steklova, 2019, Volume 307, Pages 148–179 (Mi tm4040)  

Classification of Degenerations and Picard Lattices of Kählerian K3 Surfaces with Symplectic Automorphism Group $C_4$

Viacheslav V. Nikulinab

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX, UK

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—$D_6$, $C_4$, $(C_2)^2$, $C_3$, $C_2$, and $C_1$—the classification was not completed because each of these cases requires very long and difficult considerations and calculations. The case of $D_6$ 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 $C_4$ of order $4$.

DOI: https://doi.org/10.4213/tm4040

Full text: PDF file (328 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 307, 130–161

Bibliographic databases:

UDC: 512.774+515.173.4+512.722+512.647.2
Received: February 22, 2019
Revised: February 24, 2019
Accepted: June 29, 2019

Citation: Viacheslav V. Nikulin, “Classification of Degenerations and Picard Lattices of Kählerian K3 Surfaces with Symplectic Automorphism Group $C_4$”, Algebra, number theory, and algebraic geometry, Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich, Tr. Mat. Inst. Steklova, 307, Steklov Mathematical Institute of RAS, Moscow, 2019, 148–179; Proc. Steklov Inst. Math., 307 (2019), 130–161

Citation in format AMSBIB
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\by Viacheslav~V.~Nikulin
\paper Classification of Degenerations and Picard Lattices of K\"ahlerian K3 Surfaces with Symplectic Automorphism Group $C_4$
\inbook Algebra, number theory, and algebraic geometry
\bookinfo Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich
\serial Tr. Mat. Inst. Steklova
\yr 2019
\vol 307
\pages 148--179
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4040}
\crossref{https://doi.org/10.4213/tm4040}
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\jour Proc. Steklov Inst. Math.
\yr 2019
\vol 307
\pages 130--161
\crossref{https://doi.org/10.1134/S0081543819060087}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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