On surfaces with $p_{g} = q = 2$, $K^{2} = 5$ and Albanese map of degree 3

Abstract

We construct a connected, irreducible component of the moduli space of minimal surfaces of general type with $p_{g} = q = 2$ and $K^{2} = 5$, which contains both examples given by Chen--Hacon and the first author. This component is generically smooth of dimension $4$, and all its points parametrize surfaces whose Albanese map is a generically finite triple cover.