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

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 298, Pages 144–164
DOI: https://doi.org/10.1134/S0371968517030116 (Mi tm3811)

This article is cited in 6 scientific papers (total in 6 papers)

On

$G$ -Rigid Surfaces

Vik. S. Kulikov^a, E. I. Shustin^b

^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

Full-text PDF (345 kB) Citations (6)

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

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.

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).

Received: December 26, 2016

English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 298, Pages 133–151
DOI: https://doi.org/10.1134/S0081543817060116

Bibliographic databases:

Document Type: Article

UDC: 512.774

Language: Russian

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

Citation in format AMSBIB

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\pages 144--164

\publ MAIK Nauka/Interperiodica

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Linking options:

https://www.mathnet.ru/eng/tm3811

https://doi.org/10.1134/S0371968517030116

https://www.mathnet.ru/eng/tm/v298/p144

This publication is cited in the following 6 articles:

Vik. S. Kulikov, “On the local fundamental group of the complement of a curve in a normal surface”, Izv. Math., 87:3 (2023), 562–585
Vik. S. Kulikov, “Rigid germs of finite morphisms of smooth surfaces and rational Belyi pairs”, Sb. Math., 212:9 (2021), 1304–1328
Vik. S. Kulikov, “On the variety of the inflection points of plane cubic curves”, Izv. Math., 83:4 (2019), 770–795
Vik. S. Kulikov, “On divisors of small canonical degree on Godeaux surfaces”, Sb. Math., 209:8 (2018), 1155–1163
V. L. Popov, “Compressible finite groups of birational automorphisms”, Dokl. Math., 98:2 (2018), 413–415
V. L. Popov, “The Jordan Property for Lie Groups and Automorphism Groups of Complex Spaces”, Math. Notes, 103:5 (2018), 811–819

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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