标题： 某些例外类型齐次流形上的齐次Ulrich丛 显示英文标题

标题： Homogeneous Ulrich bundles on homogenous varieties of certain exceptional types

摘要： 本文研究了有理齐次流形上齐次向量丛的Ulrich性质。 我们提供了一个准则，用于判断具有任意Picard数的有理齐次流形上的初始不可约齐次向量丛是否相对于任何极化为Ulrich。 该准则扩展了Fonarev的结果，该结果适用于Picard数为一的有理齐次流形。 作为应用，我们表明某些例外代数群的Picard数至少为二的有理齐次流形不相对于最小充分类存在这样的齐次Ulrich丛。 显示英文摘要

摘要： 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.