The classification of minimal product-quotient surfaces with $p_g=0$
Algebraic Geometry
2011-04-06 v2 Group Theory
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.
Keywords
Cite
@article{arxiv.1006.3209,
title = {The classification of minimal product-quotient surfaces with $p_g=0$},
author = {Ingrid Bauer and Roberto Pignatelli},
journal= {arXiv preprint arXiv:1006.3209},
year = {2011}
}
Comments
59 pages. v2: exposition improved