论文标题
舒伯特品种在理性的同质流形中的舒尔特刚度
Schur rigidity of Schubert varieties in rational homogeneous manifolds of Picard number one
论文作者
论文摘要
Given a rational homogeneous manifold $S=G/P$ of Picard number one and a Schubert variety $S_0 $ of $S$, the pair $(S,S_0)$ is said to be homologically rigid if any subvariety of $S$ having the same homology class as $S_0$ must be a translate of $S_0$ by the automorphism group of $S$.如果有$ s_0 $的同源类别的$ s $与同源类等于$ s_0 $的倍数，则对$（s，s_0）$被认为是刚性的刚性。早些时候，我们完全确定了同源性刚性对$（s，s_0）$，以防$ s_0 $是同质的，并在平滑的非均匀情况下回答了同样的问题。在本文中，我们考虑了Schur刚性，证明$（s，s_0）$每当$ s_0 $都是非线性平滑的Schubert品种时表现出Schur刚度。
Given a rational homogeneous manifold $S=G/P$ of Picard number one and a Schubert variety $S_0 $ of $S$, the pair $(S,S_0)$ is said to be homologically rigid if any subvariety of $S$ having the same homology class as $S_0$ must be a translate of $S_0$ by the automorphism group of $S$. The pair $(S,S_0)$ is said to be Schur rigid if any subvariety of $ S$ with homology class equal to a multiple of the homology class of $S_0$ must be a sum of translates of $S_0$. Earlier we completely determined homologically rigid pairs $(S,S_0)$ in case $S_0 $ is homogeneous and answered the same question in smooth non-homogeneous cases. In this article we consider Schur rigidity, proving that $(S,S_0)$ exhibits Schur rigidity whenever $S_0$ is a non-linear smooth Schubert variety.
