Note on a family of surfaces with $p_g=q=2$ and $K^2=7$

Matteo Penegini, Roberto Pignatelli

Published 2020-12-10, updated 2020-12-17Version 2

We study a family of surfaces of general type with $p_g=q=2$ and $K^2=7$, originally constructed by C. Rito. We provide an alternative construction of these surfaces, that allows us to describe their Albanese map and the corresponding locus $\mathcal{M}$ in the moduli space of the surfaces of general type. In particular we prove that $\mathcal{M}$ is an irreducible component, two dimensional and generically smooth.