Moduli of linear slices of high degree hypersurfaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866914982319357952 |
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| author | Patel, Anand Riedl, Eric Tseng, Dennis |
| author_facet | Patel, Anand Riedl, Eric Tseng, Dennis |
| contents | We study the variation of linear sections of hypersurfaces in $\mathbb{P}^n$. We completely classify all plane curves, necessarily singular, whose line sections do not vary maximally in moduli. In higher dimensions, we prove that the family of hyperplane sections of any smooth degree $d$ hypersurface in $\mathbb{P}^n$ vary maximally for $d \geq n+3$. In the process, we generalize the classical Grauert-Mulich theorem about lines in projective space, both to $k$-planes in projective space and to free rational curves on arbitrary varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_03689 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Moduli of linear slices of high degree hypersurfaces Patel, Anand Riedl, Eric Tseng, Dennis Algebraic Geometry We study the variation of linear sections of hypersurfaces in $\mathbb{P}^n$. We completely classify all plane curves, necessarily singular, whose line sections do not vary maximally in moduli. In higher dimensions, we prove that the family of hyperplane sections of any smooth degree $d$ hypersurface in $\mathbb{P}^n$ vary maximally for $d \geq n+3$. In the process, we generalize the classical Grauert-Mulich theorem about lines in projective space, both to $k$-planes in projective space and to free rational curves on arbitrary varieties. |
| title | Moduli of linear slices of high degree hypersurfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2005.03689 |