On Ulrich bundles on projective bundles

TL;DR

This paper investigates the existence of Ulrich bundles on projective bundles over curves and surfaces, establishing relationships with base varieties and demonstrating their existence in various cases.

Contribution

It provides new results linking Ulrich bundles on projective bundles to those on base varieties, expanding known existence results for these bundles.

Findings

Ulrich bundles exist on many projective bundles over curves and surfaces.

A relationship between Ulrich bundles on the base and on the projective bundle is established.

Existence results depend on specific polarizations.

Abstract

In this article, the existence of Ulrich bundles on projective bundles $\mathbb P(E) \to X$ is discussed. In the case, that the base variety $X$ is a curve or surface, a close relationship between Ulrich bundles on $X$ and those on $\mathbb P(E)$ is established for specific polarisations. This yields the existence of Ulrich bundles on a wide range of projective bundles over curves and surfaces.