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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 294, Pages 105–140
DOI: https://doi.org/10.1134/S0371968516030079
(Mi tm3736)
 

This article is cited in 4 scientific papers (total in 4 papers)

Plane rational quartics and K3 surfaces

Vik. S. Kulikov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (462 kB) Citations (4)
References:
Abstract: We study actions of the symmetric group $\mathbb S_4$ on K3 surfaces $X$ that satisfy the following condition: there exists an equivariant birational contraction $\overline r\colon X\to\overline X$ to a K3 surface $\overline X$ with ADE singularities such that the quotient space $\overline X/\mathbb S_4$ is isomorphic to $\mathbb P^2$. We prove that up to smooth equivariant deformations there exist exactly 15 such actions of the group $\mathbb S_4$ on K3 surfaces, and that these actions are realized as actions of the Galois groups on the Galoisations $\overline X$ of the dualizing coverings of the plane which are associated with plane rational quartics without $A_4$, $A_6$, and $E_6$ singularities as their singular points.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.
Received: March 30, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 294, Pages 95–128
DOI: https://doi.org/10.1134/S0081543816060079
Bibliographic databases:
Document Type: Article
UDC: 512.77
Language: Russian
Citation: Vik. S. Kulikov, “Plane rational quartics and K3 surfaces”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Trudy Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 105–140; Proc. Steklov Inst. Math., 294 (2016), 95–128
Citation in format AMSBIB
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\pages 105--140
\publ MAIK Nauka/Interperiodica
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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