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arXiv · 1105.4983

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

Matteo Penegini·Francesco Polizzi
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Abstract

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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Matteo Penegini, Francesco Polizzi. 2011-05-25. Surfaces with p_g=q=2, K^2=6 and Albanese map of degree 2. https://doi.org/10.4153/cjm-2012-007-0

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