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.
Original language | English |
---|---|
Pages (from-to) | 133-151 |
Number of pages | 19 |
Journal | Proceedings of the Steklov Institute of Mathematics |
Volume | 298 |
Issue number | 1 |
DOIs | |
State | Published - 1 Aug 2017 |