Normal bundles of rational curves in Grassmannians
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910407385415680 |
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| author | Coskun, Izzet Larson, Eric Vogt, Isabel |
| author_facet | Coskun, Izzet Larson, Eric Vogt, Isabel |
| contents | In projective space over fields of characteristic different from 2, the normal bundle of a general nondegenerate rational curve is balanced. The corresponding statement for rational curves in other Grassmannians can fail. Nevertheless, we prove that the normal bundle of a general rational curve in a Grassmannian decomposes into a direct sum of line bundles whose degrees are at most 2 apart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normal bundles of rational curves in Grassmannians Coskun, Izzet Larson, Eric Vogt, Isabel Algebraic Geometry 14H60, 14M15 In projective space over fields of characteristic different from 2, the normal bundle of a general nondegenerate rational curve is balanced. The corresponding statement for rational curves in other Grassmannians can fail. Nevertheless, we prove that the normal bundle of a general rational curve in a Grassmannian decomposes into a direct sum of line bundles whose degrees are at most 2 apart. |
| title | Normal bundles of rational curves in Grassmannians |
| topic | Algebraic Geometry 14H60, 14M15 |
| url | https://arxiv.org/abs/2404.08102 |