On Ulrich bundles on projective bundles

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.

15 pages. Same content as published version. There is an error in Proposition 5.13, added an erratum which will be published (separately) in Beträge zur Algebra und Geometrie (doi:10.1007/s13366-025-00786-x)