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Browsing by Author "Tarigradschi, Mihail"

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    The isomorphism problem for Grassmannian Schubert varieties
    Tarigradschi, Mihail; Xu, Weihong (Academic Press – Elsevier, 2023-11-01)
    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.