On Ulrich bundles on projective bundles

Abstract

In this article, the existence of Ulrich bundles on projective bundles {{mathbb {P}}}({{mathcal {E}}}) rightarrow 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}}}({{mathcal {E}}}) is established for specific polarisations. This yields the existence of Ulrich bundles on a wide range of projective bundles over curves and some surfaces.