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This article is cited in 6 scientific papers (total in 6 papers)
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.
Keywords:
automorphisms of algebraic surfaces, $G$-rigid surfaces, projectively rigid plane curves, dualizing coverings of the projective plane.
Received: December 26, 2016
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, Trudy Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 144–164; Proc. Steklov Inst. Math., 298 (2017), 133–151
Linking options:
https://www.mathnet.ru/eng/tm3811https://doi.org/10.1134/S0371968517030116 https://www.mathnet.ru/eng/tm/v298/p144
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