Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 107904 |
| Fachzeitschrift | Journal of Pure and Applied Algebra |
| Jahrgang | 229 |
| Ausgabenummer | 2 |
| Frühes Online-Datum | 7 Feb. 2025 |
| Publikationsstatus | Veröffentlicht - Feb. 2025 |
Abstract
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Journal of Pure and Applied Algebra, Jahrgang 229, Nr. 2, 107904, 02.2025.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Low degree rational curves on quasi-polarized K3 surfaces
AU - Rams, Sławomir
AU - Schütt, Matthias
N1 - Publisher Copyright: © 2025
PY - 2025/2
Y1 - 2025/2
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 - Elliptic fibration
KW - Hyperbolic lattice
KW - K3 surface
KW - Parabolic lattice
KW - Polarization
KW - Rational curve
UR - http://www.scopus.com/inward/record.url?scp=85217641979&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2025.107904
DO - 10.1016/j.jpaa.2025.107904
M3 - Article
VL - 229
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 2
M1 - 107904
ER -