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arXiv · 2506.06260

Elliptic constant cycle curves on Kummer surfaces

Jiexiang Huang
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Abstract

The order of a constant cycle curve $C \subset X$ on a 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 $J_{\mathrm{tr}}^3(X \times C)$. As a consequence, every $n \in \mathbb{N}$ can be realized as the order of a constant cycle curve on a K3 surface.

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Jiexiang Huang. 2025-06-06. Elliptic constant cycle curves on Kummer surfaces. https://arxiv.org/abs/2506.06260

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