The classification of surfaces with p_g = q = 0 isogenous to a product of curves

Ingrid Bauer; Fabrizio Catanese; Fritz Grunewald

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The classification of surfaces with p_g = q = 0 isogenous to a product of curves

Ingrid Bauer·Fabrizio Catanese·Fritz Grunewald

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Abstract

We classify all the surfaces with p_g = q = 0 which admit an unramified covering which is isomorphic to a product of curves. Beyond the trivial case \PP^1 x \PP^1 we find 17 families which we explicitly describe. We reduce the problem to a combinatorial description of certain generating systems for finite groups which we solve using also MAGMA's library of groups of small order.

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Ingrid Bauer, Fabrizio Catanese, Fritz Grunewald. 2006-10-08. The classification of surfaces with p_g = q = 0 isogenous to a product of curves. https://arxiv.org/abs/math/0610267

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