# Ulrich bundles on the degree six Segre fourfold

## TL;DR

This paper investigates Ulrich bundles on the Segre fourfold, providing characterizations, constructions, and conditions for their properties, advancing understanding of vector bundles in algebraic geometry.

## Contribution

It offers new characterizations and constructions of Ulrich bundles on the Segre fourfold, including those obtained as pullbacks and satisfying specific cohomological conditions.

## Key findings

- Characterization of Ulrich bundles with certain cohomological vanishing
- Construction of complex examples of Ulrich bundles
- Identification of pullback Ulrich bundles from b2

## Abstract

We study the resolution of an Ulrich bundle of arbitrary rank on the Segre fourfold $\PP^2\times\PP^2$. We characterize the Ulrich bundles $\Vv$ of arbitrary rank on $\PP^2\times\PP^2$ with $h^1(\Vv\otimes\Omega\boxtimes\Omega)=0$ or with $h^2(\Vv\otimes\Omega(-1)\boxtimes\Omega(-1))=0$ or obtained as pullback from $\PP^2$ and we construct more complicated examples.