Toric Schubert Varieties in Partial Flag Varieties
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917454323646464 |
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| author | Can, Mahir Bilen Nayek, Arpita Saha, Pinakinath |
| author_facet | Can, Mahir Bilen Nayek, Arpita Saha, Pinakinath |
| contents | In this article, we investigate the toric Schubert varieties in partial flag varieties $G/P$ for a connected semisimple algebraic group $G$. Using Deodhar's decomposition of Richardson varieties and the work of Pasquier, we give an explicit description of the fan of a toric Schubert variety, leading to a combinatorial model for its cones. As an application, we obtain necessary and sufficient conditions for smoothness of toric Schubert varieties in terms of the Cartan integers associated to a reduced expression. Furthermore, we prove that for a Coxeter-type element $w \in W^P$, the interval $[e,w]_{W^P}$ is a supersolvable join-distributive lattice. Finally, we apply these results to the study of spherical and horospherical Schubert varieties, providing a combinatorial method for checking the smoothness via the associated toric Schubert varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01332 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toric Schubert Varieties in Partial Flag Varieties Can, Mahir Bilen Nayek, Arpita Saha, Pinakinath Combinatorics Algebraic Geometry 14M15, 14M25 In this article, we investigate the toric Schubert varieties in partial flag varieties $G/P$ for a connected semisimple algebraic group $G$. Using Deodhar's decomposition of Richardson varieties and the work of Pasquier, we give an explicit description of the fan of a toric Schubert variety, leading to a combinatorial model for its cones. As an application, we obtain necessary and sufficient conditions for smoothness of toric Schubert varieties in terms of the Cartan integers associated to a reduced expression. Furthermore, we prove that for a Coxeter-type element $w \in W^P$, the interval $[e,w]_{W^P}$ is a supersolvable join-distributive lattice. Finally, we apply these results to the study of spherical and horospherical Schubert varieties, providing a combinatorial method for checking the smoothness via the associated toric Schubert varieties. |
| title | Toric Schubert Varieties in Partial Flag Varieties |
| topic | Combinatorics Algebraic Geometry 14M15, 14M25 |
| url | https://arxiv.org/abs/2605.01332 |