Transverse linear subspaces to hypersurfaces over finite fields
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Acceso en línea: | |
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| _version_ | 1866929256874901504 |
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| author | Asgarli, Shamil Duan, Lian Lai, Kuan-Wen |
| author_facet | Asgarli, Shamil Duan, Lian Lai, Kuan-Wen |
| contents | Ballico proved that a smooth projective variety $X$ of degree $d$ over a finite field of $q$ elements admits a smooth hyperplane section if $q\geq d(d-1)^{\dim X}$. In this paper, we refine this criterion for higher codimensional linear sections on smooth hypersurfaces and for hyperplane sections on Frobenius classical hypersurfaces. We also prove a similar result for the existence of reduced hyperplane sections on reduced hypersurfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_11306 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Transverse linear subspaces to hypersurfaces over finite fields Asgarli, Shamil Duan, Lian Lai, Kuan-Wen Algebraic Geometry 14G15, 14J70, 14N05 Ballico proved that a smooth projective variety $X$ of degree $d$ over a finite field of $q$ elements admits a smooth hyperplane section if $q\geq d(d-1)^{\dim X}$. In this paper, we refine this criterion for higher codimensional linear sections on smooth hypersurfaces and for hyperplane sections on Frobenius classical hypersurfaces. We also prove a similar result for the existence of reduced hyperplane sections on reduced hypersurfaces. |
| title | Transverse linear subspaces to hypersurfaces over finite fields |
| topic | Algebraic Geometry 14G15, 14J70, 14N05 |
| url | https://arxiv.org/abs/2008.11306 |