Quotients of products of curves, new surfaces with $p_g=0$ and their fundamental groups

Details Quotients of products of curves, new surfaces with $p_g=0$ and their fundamental groups Quotients of products of curves, new surfaces with $p_g=0$ and their fundamental groups

2008-09-19

arxiv.org/abs/0809.3420v3

Mathematics

Algebraic Geometry

v2: substantially improved and expanded version (56 pages instead of the former 37, new results and state of the art for surfa

Scientific paper

The first main purpose of this paper is to contribute to the existing knowledge about the complex projective surfaces $S$ of general type with $p_g(S) = 0$ and their moduli spaces, constructing 19 new families of such surfaces with hitherto unknown fundamental groups. We also provide a table containing all the known such surfaces with K^2 <=7. Our second main purpose is to describe in greater generality the fundamental groups of smooth projective varieties which occur as the minimal resolutions of the quotient of a product of curves by the action of a finite group. We classify, in the two dimensional case, all the surfaces with q=p_g = 0 obtained as the minimal resolution of such a quotient, having rational double points as singularities. We show that all these surfaces give evidence to the Bloch conjecture.

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