On surfaces with p_g=q=2, K^2=5 and Albanese map of degree 3

TL;DR

This paper constructs a new component of the moduli space for minimal surfaces with specific invariants, showing it contains known examples and characterizing the Albanese map as a triple cover.

Contribution

It introduces a connected component of the moduli space for surfaces with p_g=q=2, K^2=5, containing known examples, and describes the Albanese map as a degree 3 cover.

Findings

The moduli space component is generically smooth of dimension 4.

All surfaces in this component have Albanese maps as triple covers.

The component includes previously known examples by Chen-Hacon and the first author.

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.