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Some new surfaces with $p_g = q = 0$

Ingrid C. Bauer·Fabrizio M. E. Catanese
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Abstract

Motivated by a question by D. Mumford : can a computer classify all surfaces with $p_g = 0$ ? we try to show the complexity of the problem. We restrict it to the classification of the minimal surfaces of general type with $p_g = 0, K^2 = 8$ which are constructed by the Beauville construction, namely, which are quotients of a product of curves by the free action of a finite group G acting separately on each component. We think that man and computer will soon solve this classification problem. In the paper we classify completely the 5 cases where the group G is abelian. For these surfaces, we describe the moduli space (sometimes it is just a real point), and the first homology group. We describe also 5 examples where the group G is non abelian. Three of the latter examples had been previously described by R. Pardini.

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Ingrid C. Bauer, Fabrizio M. E. Catanese. 2003-12-12. Some new surfaces with $p_g = q = 0$. https://arxiv.org/abs/math/0310150

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