Details
| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 12 Mar 2024 |
Abstract
Keywords
- math.AG, Primary: 14J28, Secondary 14J27, 14C20
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
2024.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - Low degree rational curves on quasi-polarized K3 surfaces
AU - Rams, Sławomir
AU - Schütt, Matthias
N1 - 24 pages
PY - 2024/3/12
Y1 - 2024/3/12
N2 - 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.
AB - 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.
KW - math.AG
KW - Primary: 14J28, Secondary 14J27, 14C20
M3 - Preprint
BT - Low degree rational curves on quasi-polarized K3 surfaces
ER -