Low degree rational curves on quasi-polarized K3 surfaces

Sławomir Rams; Matthias Schütt

paper

Low degree rational curves on quasi-polarized K3 surfaces

arXiv:2403.08064

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.

24 pages