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arXiv · 1207.3526

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

Matteo Penegini·Francesco Polizzi
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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 $\mathscr{H}_3$.

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Matteo Penegini, Francesco Polizzi. 2014-09-16. A new family of surfaces with $p_g=q=2$ and $K^2=6$ whose Albanese map has degree $4$. https://doi.org/10.1112/jlms%2Fjdu048

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