Twelve Rational curves on Enriques surfaces

Given d ∈ N , we prove that any polarized Enriques surface (over any field k of characteristic p ≠ 2 or with a smooth K3 cover) of degree greater than 12 d 2 contains at most 12 rational curves of degree at most d . For d > 2 , we construct examples of Enriques surfaces of high degree that contai...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Research in the mathematical sciences 2021-06, Vol.8 (2), Article 22
Hauptverfasser:	Rams, Sławomir, Schütt, Matthias
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Computational Mathematics and Numerical Analysis Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	Given d ∈ N , we prove that any polarized Enriques surface (over any field k of characteristic p ≠ 2 or with a smooth K3 cover) of degree greater than 12 d 2 contains at most 12 rational curves of degree at most d . For d > 2 , we construct examples of Enriques surfaces of high degree that contain exactly 12 rational degree- d curves.
ISSN:	2522-0144 2197-9847
DOI:	10.1007/s40687-021-00262-7