A remark on the conjecture of Donagi-Morrison
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913595459108864 |
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| author | Watanabe, Kenta |
| author_facet | Watanabe, Kenta |
| contents | Let $X$ be a K3 surface, let $C$ be a smooth curve of genus $g$ on $X$, and let $A$ be a base point free and primitive line bundle $g_d^r$ on $C$ with $d\geq4$ and $r\geq\sqrt{\frac{d}{2}}$. In this paper, we prove that if $g>2d-3+(r-1)^2$, then there exists a line bundle $N$ on $X$ which is adapted to $|C|$ such that $|A|$ is contained in the linear system $|N\otimes\mathcal{O}_C|$, and ${\rm{Cliff}}(N\otimes\mathcal{O}_C)\leq {\rm{Cliff}}(A)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02256 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A remark on the conjecture of Donagi-Morrison Watanabe, Kenta Algebraic Geometry 14J28, 14J60, 14H60 Let $X$ be a K3 surface, let $C$ be a smooth curve of genus $g$ on $X$, and let $A$ be a base point free and primitive line bundle $g_d^r$ on $C$ with $d\geq4$ and $r\geq\sqrt{\frac{d}{2}}$. In this paper, we prove that if $g>2d-3+(r-1)^2$, then there exists a line bundle $N$ on $X$ which is adapted to $|C|$ such that $|A|$ is contained in the linear system $|N\otimes\mathcal{O}_C|$, and ${\rm{Cliff}}(N\otimes\mathcal{O}_C)\leq {\rm{Cliff}}(A)$. |
| title | A remark on the conjecture of Donagi-Morrison |
| topic | Algebraic Geometry 14J28, 14J60, 14H60 |
| url | https://arxiv.org/abs/2412.02256 |