Intersections of Schubert varieties and smooth $T$-stable subvarieties of flag varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911024230170624 |
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| author | Hong, Jaehyun Lee, Eunjeong Park, Seonjeong |
| author_facet | Hong, Jaehyun Lee, Eunjeong Park, Seonjeong |
| contents | A smooth projective variety with an action of a torus admits a cell decomposition, called the Bialynicki-Birula decomposition. Singularities of the closures of these cells are not well-known. One of the examples of such closures is a Schubert variety in a flag variety G/B, and there are several criteria for the smoothness of Schubert varieties. In this paper, we focus on the closures of Bialynicki-Birula cells in regular semisimple Hessenberg varieties Hess(s,h), called Hessenberg Schubert varieties. We first consider the intersection of the Schubert varieties with Hess(s,h) and investigate the irreducibility and the smoothness of this intersection, from which we get a sufficient condition for a Hessenberg Schubert variety to be smooth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21180 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersections of Schubert varieties and smooth $T$-stable subvarieties of flag varieties Hong, Jaehyun Lee, Eunjeong Park, Seonjeong Algebraic Geometry Primary 14M15, Secondary 05E14, 14L30 A smooth projective variety with an action of a torus admits a cell decomposition, called the Bialynicki-Birula decomposition. Singularities of the closures of these cells are not well-known. One of the examples of such closures is a Schubert variety in a flag variety G/B, and there are several criteria for the smoothness of Schubert varieties. In this paper, we focus on the closures of Bialynicki-Birula cells in regular semisimple Hessenberg varieties Hess(s,h), called Hessenberg Schubert varieties. We first consider the intersection of the Schubert varieties with Hess(s,h) and investigate the irreducibility and the smoothness of this intersection, from which we get a sufficient condition for a Hessenberg Schubert variety to be smooth. |
| title | Intersections of Schubert varieties and smooth $T$-stable subvarieties of flag varieties |
| topic | Algebraic Geometry Primary 14M15, Secondary 05E14, 14L30 |
| url | https://arxiv.org/abs/2506.21180 |