Surfaces with K^2<3\chi and finite fundamental group
Algebraic Geometry
2007-06-14 v1
Abstract
In this paper we continue the study of algebraic fundamentale group of minimal surfaces of general type S satisfying K_S^2<3\chi(S). We show that, if K_S^2= 3\chi(S)-1 and the algebraic fundamental group of S has order 8, then S is a Campedelli surface. In view of the results of math.AG/0512483 and math.AG/0605733, this implies that the fundamental group of a surface with K^2<3\chi that has no irregular etale cover has order at most 9, and if it has order 8 or 9, then S is a Campedelli surface. To obtain this result we establish some classification results for minimal surfaces of general type such that K^2=3p_g-5 and such that the canonical map is a birational morphism. We also study rational surfaces with a Z_2^3-action.
Cite
@article{arxiv.0706.1784,
title = {Surfaces with K^2<3\chi and finite fundamental group},
author = {Ciro Ciliberto and Margarida Mendes Lopes and Rita Pardini},
journal= {arXiv preprint arXiv:0706.1784},
year = {2007}
}