# On the existence of Ulrich vector bundles on some irregular surfaces

## TL;DR

This paper proves the existence of rank two Ulrich vector bundles on certain irregular surfaces, including some of general type, expanding the known classes of surfaces with such bundles.

## Contribution

It establishes the first known examples of Ulrich bundles on irregular surfaces of general type and broadens the understanding of their existence on various irregular surfaces.

## Key findings

- Existence of rank two Ulrich bundles on surfaces of maximal Albanese dimension.
- Existence of such bundles on surfaces with irregularity 1.
- Every surface with q ≤ 1 or with minimal model of rank one admits a simple rank two Ulrich bundle.

## Abstract

We establish the existence of rank two Ulrich vector bundles on surfaces that are either of maximal Albanese dimension or with irregularity 1, under many embeddings. In particular we get the first known examples of Ulrich vector bundles on irregular surfaces of general type. Another consequence is that every surface such that either $q \le 1$ or $q \ge 2$ and its minimal model has rank one, carries a simple rank two Ulrich vector bundle.