Low degree rational curves on quasi-polarized K3 surfaces

Sławomir Rams; Matthias Schütt

doi:10.1016/j.jpaa.2025.107904

Low degree rational curves on quasi-polarized K3 surfaces

Sławomir Rams^*, Matthias Schütt

^*Korrespondierende*r Autor*in für diese Arbeit

Jagiellonian University

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Abstract

We prove that there are at most (24−r0) low-degree rational curves 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 various values of r0 our bound cannot be improved.

Originalsprache	Englisch
Aufsatznummer	107904
Seitenumfang	21
Fachzeitschrift	Journal of Pure and Applied Algebra
Jahrgang	229
Ausgabenummer	2
Frühes Online-Datum	7 Feb. 2025
DOIs	https://doi.org/10.1016/j.jpaa.2025.107904 https://doi.org/10.48550/arXiv.2403.08064
Publikationsstatus	Veröffentlicht - Feb. 2025

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie

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KW - Hyperbolic lattice

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KW - Parabolic lattice

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