2023/11/01 by Yusuke Nakayama, Nakayama, Yusuke
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2311.00361
openalex publication_date 2023/11/01 · openalex created_date 2023/11/03 · openalex updated_date 2026/07/28
This paper studies the Ulrich property of homogeneous vector bundles on rational homogenous varieties. We provide a criterion for an initialized irreducible homogeneous vector bundle on a rational homogeneous variety with any Picard number to be Ulrich with respect to any polarizations. This criterion extends Fonarev's result, which applies to rational homogeneous varieties with Picard number one. As an application, we show that rational homogeneous varieties with Picard number at least two of certain exceptional algebraic groups do not admit such homogeneous Ulrich bundles with respect to the minimal ample class.