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arXiv · 2205.12814

The isomorphism problem for Grassmannian Schubert varieties

Mihail Tarigradschi·Weihong Xu
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Abstract

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.

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Mihail Tarigradschi, Weihong Xu. 2023-08-06. The isomorphism problem for Grassmannian Schubert varieties. https://doi.org/10.1016/j.jalgebra.2023.06.020

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