The classification of minimal product-quotient surfaces with 𝑝_{𝑔}=0

Bauer, I.; Pignatelli, R.

doi:10.1090/S0025-5718-2012-02604-4

The classification of minimal product-quotient surfaces with $p_g=0$
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by I. Bauer and R. Pignatelli PDF

Math. Comp. 81 (2012), 2389-2418 Request permission

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 $(-1)$-curves. For all of these surfaces the Bloch conjecture holds.

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