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

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 $6$.

arXiv commentThe previous version of arXiv:2201.06019 has been split into two papers. This version supersedes the first part, the second part will appear soon. v3: a few small improvements, as suggested by anonymous referee