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.
The classification of minimal product-quotient surfaces with p_g=0
Pignatelli, Roberto
2012-01-01
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.File in questo prodotto:
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