Curves on Brill-Noether special K3 surfaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912314540687360 |
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| author | Haburcak, Richard |
| author_facet | Haburcak, Richard |
| contents | Mukai showed that projective models of Brill-Noether general polarized K3 surfaces of genus $6-10$ and $12$ are obtained as linear sections of projective homogeneous varieties, and that their hyperplane sections are Brill-Noether general curves. In general, the question, raised by Knutsen, and attributed to Mukai, of whether the Brill-Noether generality of any polarized K3 surface $(S,H)$ is equivalent to the Brill-Noether generality of smooth curves $C$ in the linear system $|H|$, is still open. Using Lazarsfeld-Mukai bundle techniques, we answer this question in the affirmative for polarized K3 surfaces of genus $\leq 19$, which provides a new and unified proof even in the genera where Mukai models exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11664 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Curves on Brill-Noether special K3 surfaces Haburcak, Richard Algebraic Geometry 14J28, 14C20, 14C22, 14H51, 14J60 Mukai showed that projective models of Brill-Noether general polarized K3 surfaces of genus $6-10$ and $12$ are obtained as linear sections of projective homogeneous varieties, and that their hyperplane sections are Brill-Noether general curves. In general, the question, raised by Knutsen, and attributed to Mukai, of whether the Brill-Noether generality of any polarized K3 surface $(S,H)$ is equivalent to the Brill-Noether generality of smooth curves $C$ in the linear system $|H|$, is still open. Using Lazarsfeld-Mukai bundle techniques, we answer this question in the affirmative for polarized K3 surfaces of genus $\leq 19$, which provides a new and unified proof even in the genera where Mukai models exist. |
| title | Curves on Brill-Noether special K3 surfaces |
| topic | Algebraic Geometry 14J28, 14C20, 14C22, 14H51, 14J60 |
| url | https://arxiv.org/abs/2306.11664 |