Separable rational connectedness and $k$-plane sections of hypersurfaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911325215522816 |
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| author | Beheshti, Roya Mukhopadhyay, Shibashis Riedl, Eric |
| author_facet | Beheshti, Roya Mukhopadhyay, Shibashis Riedl, Eric |
| contents | Let X be a smooth hypersurface of degree d in P^n over an algebraically closed field of characteristic p. We show that X must be separably rationally connected and must contain a free line if either p is at least d or if p is at least d-1 and the defining equation has some partial derivative that is not too singular. We also show that X must be separably rationally connected in any characteristic if d = 4 and n is sufficiently large. Along the way, we generalize results on the spaces of k-planes in X to characteristic p and connect some of these questions to the spaces of linear sections of X. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15903 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Separable rational connectedness and $k$-plane sections of hypersurfaces Beheshti, Roya Mukhopadhyay, Shibashis Riedl, Eric Algebraic Geometry Let X be a smooth hypersurface of degree d in P^n over an algebraically closed field of characteristic p. We show that X must be separably rationally connected and must contain a free line if either p is at least d or if p is at least d-1 and the defining equation has some partial derivative that is not too singular. We also show that X must be separably rationally connected in any characteristic if d = 4 and n is sufficiently large. Along the way, we generalize results on the spaces of k-planes in X to characteristic p and connect some of these questions to the spaces of linear sections of X. |
| title | Separable rational connectedness and $k$-plane sections of hypersurfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.15903 |