Homogeneous Ulrich bundles on isotropic flag varieties

TL;DR

This paper investigates the existence of Ulrich bundles on certain rational homogeneous spaces, concluding that no irreducible homogeneous Ulrich bundles exist on these spaces when the Picard number is at least 2.

Contribution

It establishes a non-existence result for irreducible homogeneous Ulrich bundles on isotropic flag varieties of types B, C, and D with Picard number ≥ 2.

Findings

No irreducible homogeneous Ulrich bundles exist for Picard number ≥ 2

Results apply to spaces of types B, C, and D

Focus on minimal ample class

Abstract

In this paper, we consider the existence problem of Ulrich bundles on a rational homogeneous space $G/P$ of type $B$, $C$ or $D$. We show that if the Picard number of $G/P$ is greater than or equal to $2$, then there are no irreducible homogeneous Ulrich bundles on $G/P$ with respect to the minimal ample class.