Low degree rational curves on quasi-polarized K3 surfaces

Sławomir Rams; Matthias Schütt

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arXiv · 2403.08064

Low degree rational curves on quasi-polarized K3 surfaces

Sławomir Rams·Matthias Schütt

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Abstract

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.

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BibTeX RIS

Sławomir Rams, Matthias Schütt. 2024-03-12. Low degree rational curves on quasi-polarized K3 surfaces. https://arxiv.org/abs/2403.08064

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