Surfaces with K^2<3χand finite fundamental group

Ciliberto, Ciro; Lopes, Margarida Mendes; Pardini, Rita

Surfaces with K^2<3χand finite fundamental group

Authors

Ciliberto, Ciro

Lopes, Margarida Mendes

Pardini, Rita

Description

In this paper we continue the study of algebraic fundamentale group of minimal surfaces of general type S satisfying K_S^2<3χ(S). We show that, if K_S^2= 3χ(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<3χthat 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.
18 pages. To appear in Math. Res. Lett