Surfaces with p_g=q=2, K^2=6 and Albanese map of degree 2

Details Surfaces with p_g=q=2, K^2=6 and Albanese map of degree 2 Surfaces with p_g=q=2, K^2=6 and Albanese map of degree 2

2011-05-25

arxiv.org/abs/1105.4983v2

Mathematics

Algebraic Geometry

24 pages, 2 figures. Final version, to appear in Canadian Journal of Mathematics

Scientific paper

10.4153/CJM-2012-007-0

We classify minimal surfaces $S$ of general type with $p_g=q=2$ and $K_S^2=6$ whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth, irreducible components $\mathcal{M}_{Ia}$, $\mathcal{M}_{Ib}$, $\mathcal{M}_{II}$ of dimension 4, 4, 3, respectively. The general surface $S$ contains a smooth elliptic curve $Z$ such that $Z^2=-2$, which is contracted by the Albanese map and which is preserved by any first-order deformation.

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