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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TRSPY_2017_298_a10,
     author = {Vik. S. Kulikov and E. I. Shustin},
     title = {On $G${-Rigid} {Surfaces}},
     journal = {Informatics and Automation},
     pages = {144--164},
     publisher = {mathdoc},
     volume = {298},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_298_a10/}
}
TY  - JOUR
AU  - Vik. S. Kulikov
AU  - E. I. Shustin
TI  - On $G$-Rigid Surfaces
JO  - Informatics and Automation
PY  - 2017
SP  - 144
EP  - 164
VL  - 298
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2017_298_a10/
LA  - ru
ID  - TRSPY_2017_298_a10
ER  - 
%0 Journal Article
%A Vik. S. Kulikov
%A E. I. Shustin
%T On $G$-Rigid Surfaces
%J Informatics and Automation
%D 2017
%P 144-164
%V 298
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2017_298_a10/
%G ru
%F TRSPY_2017_298_a10
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/