On G-rigid surfaces


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详细

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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Vik. Kulikov

Steklov Mathematical Institute of Russian Academy of Sciences

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Email: kulikov@mi.ras.ru
俄罗斯联邦, ul. Gubkina 8, Moscow, 119991

E. Shustin

School of Mathematical Sciences

Email: kulikov@mi.ras.ru
以色列, Tel Aviv, 69978

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