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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29260 |
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| _version_ | 1866911556528242688 |
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| author | Gorsky, Eugene Kim, Soyeon Sherman-Bennett, Melissa |
| author_facet | Gorsky, Eugene Kim, Soyeon Sherman-Bennett, Melissa |
| contents | We prove that an open Richardson variety in the complete flag variety for $\mathrm{GL}_n$ is isomorphic to a torus if and only if the corresponding closed Richardson variety is toric. Such toric varieties can be classified in terms of the combinatorics of Bruhat intervals, and include many varieties of dimension larger than $n-1$. We give a combinatorial description of the corresponding polytopes, and compute several explicit examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29260 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unexpected toric Richardson varieties Gorsky, Eugene Kim, Soyeon Sherman-Bennett, Melissa Algebraic Geometry Combinatorics We prove that an open Richardson variety in the complete flag variety for $\mathrm{GL}_n$ is isomorphic to a torus if and only if the corresponding closed Richardson variety is toric. Such toric varieties can be classified in terms of the combinatorics of Bruhat intervals, and include many varieties of dimension larger than $n-1$. We give a combinatorial description of the corresponding polytopes, and compute several explicit examples. |
| title | Unexpected toric Richardson varieties |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2603.29260 |