Some new surfaces with p g = q = 0.
By Ingrid Bauer, F. Catanese. 2003
51 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3691a0795b5625312e563242a33c423c5e6bbe24
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The classification of isotrivially fibred surfaces with pg = q = 2 (2009, methodology): “The classification of the surfaces isogenous to a product involves techniques from both geometry and combinatorial group theory developed in [ 4 ,5,14,33].”
- Generalized Fermat curves (2009, methodology): “Bauer and Catanese [3] have proved that when G = Z(2)5 one obtains exactly two nonisomorphic complex surfaces whereas for G = Z(4)2 the complex surfaces so obtained form an irreducible connected component of dimension 4 in their moduli space.”