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

2010/06/16 by Ingrid Bauer, Bauer, Ingrid, Roberto Pignatelli +1 · 2 citations
Mathematics · #14J10 #14J25 #14J29 #14Q10 #20F99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1006.3209

openalex publication_date 2010/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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

Cited by

• Computation of Singular Godeaux Surfaces and a New Explicit Fake Quadric (With an Appendix by Christian Gleissner and Noah Ruhland)
• Obstructions to unirationality for product-quotient surfaces over \mathbbF_p

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