The curves of elliptic nodes on K3 surfaces
Abstract
Abstract Let ( X , L ) be a polarized K3 surface of genus g and $$C_{en} \subset X$$ C en ⊂ X be the curve of singular points of nodal elliptic curves in | L |. When ( X , L ) is generic of genus two, Huybrechts proved that the curve $$C_{en}$$ C en is a constant cycle curve and conjectured that this remains true for higher genus cases. In this note, we show that the conjecture holds true for polarized K3 surfaces ( X , L ) lying in a locus of codimension one in the moduli space of polarized K3 surfaces of genus g for every $$g > 2$$ g > 2
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Geometric and Algebraic Topology
Publication details
- Journal / source
- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- Volume
- 67
- Issue
- 3
- Pages
- 733–742
- Publication date
- 11 March 2026
- Language
- EN