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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.07486 |
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| _version_ | 1866915619383803904 |
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| author | Ananyevskiy, Alexey Levine, Marc |
| author_facet | Ananyevskiy, Alexey Levine, Marc |
| contents | We investigate the question of the existence of a non-vanishing section of the tangent bundle on a smooth affine quadric hypersurface $Q^o$ over a given perfect field $k$. In case $Q^o$ admits a $k$-rational point, we give necessary and sufficient conditions for such existence. We apply these conditions in a number of examples, including the case of the algebraic $n$-sphere over $k$, $S^n_k\subset \mathbb{A}^{n+1}_k$, defined by the equation $\sum_{i=1}^{n+1}x_i^2=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07486 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Combing a hedgehog over a field Ananyevskiy, Alexey Levine, Marc Algebraic Geometry 14F42, 14J60 We investigate the question of the existence of a non-vanishing section of the tangent bundle on a smooth affine quadric hypersurface $Q^o$ over a given perfect field $k$. In case $Q^o$ admits a $k$-rational point, we give necessary and sufficient conditions for such existence. We apply these conditions in a number of examples, including the case of the algebraic $n$-sphere over $k$, $S^n_k\subset \mathbb{A}^{n+1}_k$, defined by the equation $\sum_{i=1}^{n+1}x_i^2=1$. |
| title | Combing a hedgehog over a field |
| topic | Algebraic Geometry 14F42, 14J60 |
| url | https://arxiv.org/abs/2311.07486 |