On Primitive Ulrich Bundles over a few projective varieties with Picard number two

TL;DR

This paper introduces primitive Ulrich bundles on certain projective varieties, providing cohomological characterizations for specific cases and proposing open problems for further research.

Contribution

It defines primitive Ulrich bundles, offers cohomological criteria for degree 6 flag threefolds and rational normal scrolls, and suggests directions for future work.

Findings

Cohomological characterization of primitive Ulrich bundles

Application to degree 6 flag threefolds

Application to rational normal scrolls

Abstract

We introduce the notion of primitive Ulrich bundle in a smooth projective variety. We motivate this notion and give a cohomological characterization in the case of the degree $6$ flag threefold and rational normal scrolls. Finally we propose a few open problems.