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 whose canonical class has positive selfintersection which is not minimal, and describe its ( − 1 ) (-1) -curves. For all of these surfaces the Bloch conjecture holds.