Periodic sharpness of Miyaoka's bound for smooth rational curves

2025/12/05 by Degtyarev, Alex, Rams, Sławomir
#Algebraic Geometry (math.AG) #FOS: Mathematics #Primary: 14J28 #Secondary 14N25

paper · doi:10.48550/arxiv.2512.06145

Abstract

We determine the maximal number of smooth rational degree d curves on a complex K3-surface of degree 2n provided n is sufficiently large as compared to d>1. We obtain precise characterization of configurations of rational degree d curves for which Miyaoka's bound is sharp for nd odd and n sufficiently large as compared to d.

Citations

• Miyaoka's bound for conics on K3 surfaces and beyond
• Low degree rational curves on quasi-polarized K3 surfaces
• Counting Lines with Vinberg's algorithm

Related

• Miyaoka's bound for conics on K3 surfaces and beyond
• Counting rational curves on K3 surfaces
• Counting real rational curves on K3 surfaces
• Uniform Bounds for the Number of Rational Points on Symmetric Squares of Curves with Low Mordell-Weil Rank
• Rational Curves on K3 Surfaces