Minimal rational curves on complete symmetric varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908369465376768 |
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| author | Brion, Michel Kim, Shin-young Perrin, Nicolas |
| author_facet | Brion, Michel Kim, Shin-young Perrin, Nicolas |
| contents | We describe the families of minimal rational curves on any complete symmetric variety, and the corresponding varieties of minimal rational tangents (VMRT). In particular, we prove that these varieties are homogeneous and that for non-exceptional irreducible wonderful varieties, there is a unique family of minimal rational curves, and hence a unique VMRT. We relate these results to the restricted root system of the associated symmetric space. In particular we answer by the negative a question of Hwang: for certain Fano wonderful symmetric varieties, the VMRT has two connected components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03013 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimal rational curves on complete symmetric varieties Brion, Michel Kim, Shin-young Perrin, Nicolas Algebraic Geometry Representation Theory 14H10, 14M17, 17B22, 32M12 We describe the families of minimal rational curves on any complete symmetric variety, and the corresponding varieties of minimal rational tangents (VMRT). In particular, we prove that these varieties are homogeneous and that for non-exceptional irreducible wonderful varieties, there is a unique family of minimal rational curves, and hence a unique VMRT. We relate these results to the restricted root system of the associated symmetric space. In particular we answer by the negative a question of Hwang: for certain Fano wonderful symmetric varieties, the VMRT has two connected components. |
| title | Minimal rational curves on complete symmetric varieties |
| topic | Algebraic Geometry Representation Theory 14H10, 14M17, 17B22, 32M12 |
| url | https://arxiv.org/abs/2303.03013 |