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The isomorphism problem for Schubert varieties

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arxiv 2103.08114 v2 pith:IC7GYWTJ submitted 2021-03-15 math.AG math.CO

Edward Richmond , William Slofstra This is my paper · ORCID
classification math.AGmath.CO
keywords schubertvarietieselementsflaggroupisomorphicisomorphismweyl
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Schubert varieties in the full flag variety of Kac-Moody type are indexed by elements of the corresponding Weyl group. We give a practical criterion for when two such Schubert varieties (from potentially different flag varieties) are isomorphic, in terms of the Cartan matrix and reduced words for the indexing Weyl group elements. As a corollary, we show that two such Schubert varieties are isomorphic if and only if there is an isomorphism between their integral cohomology rings that preserves the Schubert basis.

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  1. An anticanonical perspective on G/P Schubert varieties

    math.AG 2025-06 conditional novelty 8.0 of 10

    For simply-laced Schubert varieties, factoriality, Q-factoriality, and a Betti number equality are equivalent, and the anticanonical line bundle is computed by an explicit coroot matrix.

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