Low degree rational curves on quasi-polarized K3 surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914711581229056 |
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| author | Rams, Sławomir Schütt, Matthias |
| author_facet | Rams, Sławomir Schütt, Matthias |
| contents | We prove that there are at most $(24-r_0)$ low-degree rational curves on high-degree models of K3 surfaces with at most Du Val singularities, where $r_0$ is the number of exceptional divisors on the minimal resolution. We also provide several existence results in the above setting (i.e. for rational curves on quasi-polarized K3 surfaces), which imply that for various values of $r_0$ our bound cannot be improved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low degree rational curves on quasi-polarized K3 surfaces Rams, Sławomir Schütt, Matthias Algebraic Geometry Primary: 14J28, Secondary 14J27, 14C20 We prove that there are at most $(24-r_0)$ low-degree rational curves on high-degree models of K3 surfaces with at most Du Val singularities, where $r_0$ is the number of exceptional divisors on the minimal resolution. We also provide several existence results in the above setting (i.e. for rational curves on quasi-polarized K3 surfaces), which imply that for various values of $r_0$ our bound cannot be improved. |
| title | Low degree rational curves on quasi-polarized K3 surfaces |
| topic | Algebraic Geometry Primary: 14J28, Secondary 14J27, 14C20 |
| url | https://arxiv.org/abs/2403.08064 |