Multi-rigidity of Schubert classes in partial flag varieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912092966092800 |
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| author | Liu, Yuxiang Sheshmani, Artan Yau, Shing-Tung |
| author_facet | Liu, Yuxiang Sheshmani, Artan Yau, Shing-Tung |
| contents | In this paper, we study the multi-rigidity problem in rational homogeneous spaces. A Schubert class is called multi-rigid if every multiple of it can only be represented by a union of Schubert varieties. We prove the multi-rigidity of Schubert classes in rational homogeneous spaces. In particular, we characterize the multi-rigid Schubert classes in partial flag varieties of type A, B and D. Moreover, for a general rational homogeneous space $G/P$, we deduce the rigidity and multi-rigidity from the corresponding generalized Grassmannians (correspond to maximal parabolics). When $G$ is semi-simple, we also deduce the rigidity and multi-rigidity from the simple cases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_21726 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-rigidity of Schubert classes in partial flag varieties Liu, Yuxiang Sheshmani, Artan Yau, Shing-Tung Algebraic Geometry 14M15, 14M17, 51M35, 32M10 In this paper, we study the multi-rigidity problem in rational homogeneous spaces. A Schubert class is called multi-rigid if every multiple of it can only be represented by a union of Schubert varieties. We prove the multi-rigidity of Schubert classes in rational homogeneous spaces. In particular, we characterize the multi-rigid Schubert classes in partial flag varieties of type A, B and D. Moreover, for a general rational homogeneous space $G/P$, we deduce the rigidity and multi-rigidity from the corresponding generalized Grassmannians (correspond to maximal parabolics). When $G$ is semi-simple, we also deduce the rigidity and multi-rigidity from the simple cases. |
| title | Multi-rigidity of Schubert classes in partial flag varieties |
| topic | Algebraic Geometry 14M15, 14M17, 51M35, 32M10 |
| url | https://arxiv.org/abs/2410.21726 |