A new family of surfaces with $p_g=q=2$ and $K^2=6$ whose Albanese map has degree $4$

Abstract

We construct a new family of minimal surfaces of general type with $p_g=q=2$ and $K^2=6$, whose Albanese map is a quadruple cover of an abelian surface with polarization of type $(1,3)$. We also show that this family provides an irreducible component of the moduli space of surfaces with $p_g=q=2$ and $K^2=6$. Finally, we prove that such a component is generically smooth of dimension 4 and that it contains the 2-dimensional family of product-quotient examples previously constructed by the first author. The main tools we use are the Fourier-Mukai transform and the Schrödinger representation of the finite Heisenberg group ${\mathcal{H}}_3$.

23 pages. To appear in the Journal of the London Mathematical Society. This is a preprint version, slightly different from the published version

References in corpus (2)

• A Superficial Working Guide to Deformations and Moduli
• Surfaces with p_g=q=2, K^2=6 and Albanese map of degree 2

Cited by in corpus (4)

• A family of surfaces with $p_g=q=2,K^2=7$ and Albanese map of degree $3$
• 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 $p_g=q=2$