Equivariant rigidity of Richardson varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916918637625344 |
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| author | Buch, Anders S. Chaput, Pierre-Emmanuel Perrin, Nicolas |
| author_facet | Buch, Anders S. Chaput, Pierre-Emmanuel Perrin, Nicolas |
| contents | We prove that Schubert and Richardson varieties in flag manifolds are uniquely determined by their equivariant cohomology classes, as well as a stronger result that replaces Schubert varieties with closures of Bialynicki-Birula cells under suitable conditions. This is used to prove that any two-pointed curve neighborhood representing a quantum cohomology product with a Seidel class is a Schubert variety. We pose a stronger conjecture which implies a Seidel multiplication formula in equivariant quantum K-theory, and prove this conjecture for cominuscule flag varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11387 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant rigidity of Richardson varieties Buch, Anders S. Chaput, Pierre-Emmanuel Perrin, Nicolas Algebraic Geometry 14M15 (Primary) 14C25, 14L30, 14N35, 14N15, 19E08 (Secondary) We prove that Schubert and Richardson varieties in flag manifolds are uniquely determined by their equivariant cohomology classes, as well as a stronger result that replaces Schubert varieties with closures of Bialynicki-Birula cells under suitable conditions. This is used to prove that any two-pointed curve neighborhood representing a quantum cohomology product with a Seidel class is a Schubert variety. We pose a stronger conjecture which implies a Seidel multiplication formula in equivariant quantum K-theory, and prove this conjecture for cominuscule flag varieties. |
| title | Equivariant rigidity of Richardson varieties |
| topic | Algebraic Geometry 14M15 (Primary) 14C25, 14L30, 14N35, 14N15, 19E08 (Secondary) |
| url | https://arxiv.org/abs/2409.11387 |