The classification of minimal product-quotient surfaces with $p_g=0$

Abstract

A product-quotient surface is the minimal resolution of the singularities of the quotient of a product of two curves by the action of a finite group acting separately on the two factors. We classify all minimal product-quotient surfaces of general type with geometric genus 0: they form 72 families. We show that there is exactly one product-quotient surface of general type with big canonical class which is not minimal, and describe its (-1) curves. For all these surfaces the Bloch conjecture holds.

arXiv comment59 pages. v2: exposition improved

References in corpus (2)

• Numerical properties of isotrivial fibrations
• Quotients of products of curves, new surfaces with $p_g=0$ and their fundamental groups

Cited by in corpus (5)

• Construction of surfaces of general type from elliptic surfaces via Q-Gorenstein smoothing
• Product-Quotient Surfaces: Result and Problems
• Involutions on surfaces with $p_g=q=0$ and $K^2=3$
• Surfaces with p_g = 0: Constructions and Moduli spaces, Burniat surfaces and deformations of automorphisms
• Unprojection and deformations of tertiary Burniat surfaces