12 rational curves on Enriques surfaces

2020/05/26 by Rams, Sławomir, Schütt, Matthias
#14C20 #14J27 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.12939

Abstract

Given d in IN, we prove that any polarized Enriques surface (over any field of characteristic different from 2 or with a smooth K3 cover) of degree greater than 12d² 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.

Related

• Singular rational curves on Enriques surfaces
• Low degree rational curves on quasi-polarized K3 surfaces
• Enriques Surfaces and jacobian elliptic K3 surfaces
• Enriques surfaces with eight nodes
• Towards refined curve counting on the Enriques surface I: K-theoretic refinements