Geodesic
On $G$-Rigid Surfaces
Informatics and Automation, Complex analysis and its applications, Tome 298 (2017), pp. 144-164.

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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. 
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     title = {On $G${-Rigid} {Surfaces}},
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Vik. S. Kulikov; E. I. Shustin. On $G$-Rigid Surfaces. Informatics and Automation, Complex analysis and its applications, Tome 298 (2017), pp. 144-164. http://geodesic.mathdoc.fr/item/TRSPY_2017_298_a10/

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