论文标题
Grassmannian Schubert品种的同构问题
The isomorphism problem for Grassmannian Schubert varieties
论文作者
论文摘要
我们证明，当且仅当其相应的年轻图与转座相同的情况下，舒伯特在潜在不同的司法的种类中都是同构的。我们还讨论了这一结果对格拉斯曼尼亚理查森品种的概括。特别是，我们证明，如果它们相应的偏斜图为posets，那么潜在不同的司法的理查森品种作为品种是同构的，并且我们猜想了相反。在这里，如果它们的连接组件之间有两次两者的两次两种态度，则可以说两个POSET是半同态的，因此相应的组件是同构或相反的。
We prove that Schubert varieties in potentially different Grassmannians are isomorphic as varieties if and only if their corresponding Young diagrams are identical up to a transposition. We also discuss a generalization of this result to Grassmannian Richardson varieties. In particular, we prove that Richardson varieties in potentially different Grassmannians are isomorphic as varieties if their corresponding skew diagrams are semi-isomorphic as posets, and we conjecture the converse. Here, two posets are said to be semi-isomorphic if there is a bijection between their sets of connected components such that the corresponding components are either isomorphic or opposite.
