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 Tr. Mat. Inst. Steklova, 2017, Volume 298, Pages 144–164 (Mi tm3811)

On $G$-Rigid Surfaces

Vik. S. Kulikova, E. I. Shustinb

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Abstract: Rigid algebraic varieties form an important class of complex varieties that exhibit interesting geometric phenomena. In this paper we propose a natural extension of rigidity to complex projective varieties with a finite group action ($G$-varieties) and focus on the first nontrivial case, namely, on $G$-rigid surfaces that can be represented as desingularizations of Galois coverings of the projective plane with Galois group $G$. We obtain local and global $G$‑rigidity criteria for these $G$-surfaces and present several series of such surfaces that are rigid with respect to the action of the deck transformation group.

 Funding Agency Grant Number German-Israeli Foundation for Scientific Research and Development 1174-197.6/2011 Israel Science Foundation 176/15 Russian Science Foundation 14-50-00005 The work presented in Section 4 was performed by Vik. S. Kulikov in the Steklov Mathematical Institute of Russian Academy of Sciences and supported by the Russian Science Foundation under grant 14-50-00005. E. I. Shustin was supported by the German–Israeli Foundation for Scientific Research and Development (project no. 1174-197.6/2011) and by the Israel Science Foundation (project no. 176/15).

DOI: https://doi.org/10.1134/S0371968517030116

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 298, 133–151

Bibliographic databases:

Document Type: Article
UDC: 512.774

Citation: Vik. S. Kulikov, E. I. Shustin, “On $G$-Rigid Surfaces”, Complex analysis and its applications, Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar, Tr. Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 144–164; Proc. Steklov Inst. Math., 298 (2017), 133–151

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3811
• https://doi.org/10.1134/S0371968517030116
• http://mi.mathnet.ru/eng/tm/v298/p144

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This publication is cited in the following articles:
1. Vik. S. Kulikov, “On divisors of small canonical degree on Godeaux surfaces”, Sb. Math., 209:8 (2018), 1155–1163
2. V. L. Popov, “Compressible finite groups of birational automorphisms”, Dokl. Math., 98:2 (2018), 413–415
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