Elliptic constant cycle curves on Kummer surfaces
Abstract
The order of a constant cycle curve $$C \subset X$$ on a complex K3 surface, defined by Huybrechts, is a positive integer that measures the obstruction to decomposing the diagonal class $$\Delta _C$$ in the Chow group $$\mathrm{CH}^2(X \times C)$$ . In this paper, we compute the order of elliptic constant cycle curves that naturally arise on Kummer surfaces, by passing to the transcendental intermediate Jacobian $$J_{\textrm{tr}}^3(X \times C)$$ . As a consequence, every $$n \in \mathbb {N}$$ can be realized as the order of a constant cycle curve on a complex K3 surface.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Publication details
- Journal / source
- Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
- Volume
- 96
- Issue
- 1
- Pages
- 73–92
- Publication date
- 1 April 2026
- Language
- EN