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

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.

11 pages. Dedicated to the memory of Gianfranco Casnati. The final version will appear on Rend. Semin. Mat., Univ. Politec. Torino