Non-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension

TL;DR

This paper classifies non-big Ulrich vector bundles on quadrics and Del Pezzo fourfolds, providing a detailed understanding of rank r Ulrich bundles with limited numerical dimension on smooth varieties.

Contribution

It offers a classification of non-big Ulrich bundles on specific varieties and describes the structure of rank r Ulrich bundles with bounded numerical dimension.

Findings

Classification of non-big Ulrich bundles on quadrics

Classification on Del Pezzo fourfold of degree 6

Description of rank r Ulrich bundles with numerical dimension ≤ n/2 + r - 1

Abstract

On any smooth $n$-dimensional variety we give a pretty precise picture of rank $r$ Ulrich vector bundles with numerical dimension at most $\frac{n}{2}+r-1$. Also, we classify non-big Ulrich vector bundles on quadrics and on the Del Pezzo fourfold of degree $6$.