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.