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

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.

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

References in corpus (3)

• A Superficial Working Guide to Deformations and Moduli
• Beauville surfaces and finite simple groups
• Galois closure and Lagrangian varieties

Cited by in corpus (9)

• A Superficial Working Guide to Deformations and Moduli
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• A new family of surfaces with $p_g=q=2$ and $K^2=6$ whose Albanese map has degree $4$
• A pair of rigid surfaces with $p_g=q=2$ and $K^2=8$ whose universal cover is not the bidisk
• Characterization of products of theta divisors
• A note on surfaces with $p_g=q=2$ and an irrational fibration
• Monodromy representations and surfaces with maximal Albanese dimension
• On the classification of surfaces of general type with $p_g=q=2$
• Surfaces with p_g = 0: Constructions and Moduli spaces, Burniat surfaces and deformations of automorphisms