Mixed surfaces, new surfaces of general type with $p_g=0$ and their fundamental group

Details Mixed surfaces, new surfaces of general type with $p_g=0$ and their fundamental group Mixed surfaces, new surfaces of general type with $p_g=0$ and their fundamental group

2011-05-06

arxiv.org/abs/1105.1259v1

Mathematics

Algebraic Geometry

47 pages

Scientific paper

We call a projective surface $X$ \no{mixed surface} if there exists a curve $C$ and a finite group $G$ that acts on $C\times C$ exchanging the factors \sts $X=(C\times C)/G$ and the map $C\times C \rightarrow X$ has finite branching locus. We study the mixed 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 mixed surfaces of general type with $p_g=0$. As an important byproduct, we provide an example of numerical Campedelli surface with topological fundamental group $\bbZ_4$, and we realize 3 new topological types of surfaces of general type. Three of the families we construct are $\bbQ$-homology projective planes.

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