A note on surfaces with $p_g=q=2$ and an irrational fibration

TL;DR

This paper explores specific algebraic surfaces with geometric genus and irregularity both equal to 2, focusing on their structure when they possess an irrational fibration and maximal Albanese dimension.

Contribution

It provides new examples and insights into surfaces with $p_g=q=2$ that have irrational fibrations and maximal Albanese dimension.

Findings

Identification of several new examples of such surfaces

Analysis of their geometric and fibration properties

Insights into the structure of surfaces with these invariants

Abstract

We study several examples of surfaces with $p_g = q = 2$ and maximal Albanese dimension that are endowed with an irrational fibration.