Some evidence for the existence of Ulrich bundles

TL;DR

The paper investigates the existence of Ulrich bundles on nonsingular projective varieties through K-theoretic and derived category approaches, proposing new methods and observations for constructing such bundles.

Contribution

It introduces a K-theoretic perspective and a derived category approach to the existence problem of Ulrich bundles, offering new avenues for their construction.

Findings

If motivic vector bundles are algebraic, a solution exists in the Grothendieck group.

A formal method is proposed for producing Ulrich sheaves on surfaces.

Abstract

The question of existence of Ulrich bundles on nonsingular projective varieties is posed here in weaker terms: either to find a K-theoretic solution, or to find one in the derived category of the variety. We observe that if any motivic vector bundle is algebraic, there is always a solution in the Grothendieck group. Also, by considering the derived problem, it is noted a formal way of producing Ulrich sheaves on a surface.