Mixed quasi-étale surfaces, new surfaces of general type with p_g=0 and their fundamental group

• Autores: Davide Frapporti
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 64, Fasc. 3, 2013, págs. 293-311
• Idioma: inglés
• DOI: 10.1007/s13348-013-0084-5
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• Resumen

  • We call a projective surface X mixed quasi-étale quotient if there exists a curve C of genus g(C)\ge 2 and a finite group G that acts on C\times C exchanging the factors such that X=(C\times C)/G and the map C\times C \rightarrow X has finite branch locus. The minimal resolution of its singularities is called mixed quasi-étale surface. We study the mixed quasi-étale surfaces under the assumption that (C\times C)/G^0 has only nodes as singularities, where G^0\triangleleft G is the index two subgroup of the elements that do not exchange the factors. We classify the minimal regular surfaces with p_g=0 whose canonical model is a mixed quasi-étale quotient as above. All these surfaces are of general type and as an important byproduct, we provide an example of a numerical Campedelli surface with topological fundamental group \mathbb{Z }_4, and we realize 2 new topological types of surfaces of general type. Three of the families we construct are \mathbb{Q }-homology projective planes.