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

TL;DR

This paper provides a near-complete classification of non-big Ulrich vector bundles on fourfolds, including specific cases like Picard rank one, Mukai, and Del Pezzo fourfolds, advancing understanding in algebraic geometry.

Contribution

It offers the first comprehensive classification of non-big Ulrich bundles on fourfolds and their determinants on certain classes of fourfolds, filling a significant gap in the literature.

Findings

Classified non-big Ulrich bundles on Picard rank one fourfolds

Classified Ulrich bundles with non-big determinant on Del Pezzo and Mukai fourfolds

Extended classification to Del Pezzo n-folds for n ≤ 4

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 $n \le 4$. We also classify Ulrich bundles with non-big determinant on Del Pezzo and Mukai $n$-folds, $n \ge 2$.