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

Abstract

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.

v2: substantially improved and expanded version (56 pages instead of the former 37, new results and state of the art for surfaces with p_g =0). v3: title change

References in corpus (2)

• A simply connected surface of general type with p_g=0 and K^2=2
• Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces

Cited by in corpus (7)

• Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces
• The classification of minimal product-quotient surfaces with $p_g=0$
• Some (big) irreducible components of the moduli space of minimal surfaces of general type with $p_g=q=1$ and $K^2=4$
• Product-Quotient Surfaces: Result and Problems
• Compact Kähler manifolds with elliptic homotopy type
• A surface of general type with p_g=0 and K^2=8 whose universal cover is not the bidisc
• Surfaces with p_g = 0: Constructions and Moduli spaces, Burniat surfaces and deformations of automorphisms