On the classification of non-big Ulrich vector bundles on fourfolds

Abstract

We give an almost complete classification of non-big Ulrich vector bundles on fourfolds. This allows to classify them in the case of Picard rank one fourfolds, of Mukai fourfolds and in the case of Del Pezzo n-folds for n ≤ 4. We also classify Ulrich bundles with non-big determinant on Del Pezzo and Mukai n-folds, n ≥ 2.