Low degree rational curves on quasi-polarized K3 surfaces

Low degree rational curves on quasi-polarized K3 surfaces

We prove that there are at most (24−r0) irreducible rational curves of positive low-degree on high-degree models of K3 surfaces with at most Du Val singularities, where r0 is the number of exceptional divisors on the minimal resolution. We also provide several existence results in the above setting...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of pure and applied algebra 2025-02, p.107904, Article 107904
Hauptverfasser: Rams, Sławomir, Schütt, Matthias
Format: Artikel
Sprache:eng
Schlagworte:
Elliptic fibration
Hyperbolic lattice
K3 surface
Parabolic lattice
Polarization
Rational curve
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We prove that there are at most (24−r0) irreducible rational curves of positive low-degree on high-degree models of K3 surfaces with at most Du Val singularities, where r0 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 many values of r0 our bound cannot be improved.
ISSN:0022-4049
DOI:10.1016/j.jpaa.2025.107904