On <Emphasis Type="Italic">G</Emphasis>-rigid surfaces |
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Authors: | Email author" target="_blank">Vik?S?KulikovEmail author E?I?Shustin |
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Institution: | 1.Steklov Mathematical Institute of Russian Academy of Sciences,Moscow,Russia;2.School of Mathematical Sciences,Tel Aviv University,Tel Aviv,Israel |
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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. |
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