Surfaces with K^2<3χand finite fundamental group

Details Surfaces with K^2<3χand finite fundamental group Surfaces with K^2<3χand finite fundamental group

2007-06-12

arxiv.org/abs/0706.1784v1

Mathematics

Algebraic Geometry

18 pages. To appear in Math. Res. Lett

Scientific paper

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.

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