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arXiv · 2407.01304

Heights of Ceresa and Gross-Schoen cycles

Ziyang Gao·Shou-Wu Zhang
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Abstract

We study the Beilinson-Bloch heights of Ceresa and Gross-Schoen cycles in families. We construct that for any $g\ge 3$, a Zariski open dense subset $\mathcal{M}_g^{\mathrm{amp}}$ of $\mathcal{M}_g$, the coarse moduli of curves of genus $g$ over $\mathbb{Q}$, such that the heights of Ceresa cycles and Gross-Schoen cycles over $\mathcal{M}_g^{\mathrm{amp}}$ have a lower bound and satisfy the Northcott property.

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Ziyang Gao, Shou-Wu Zhang. 2024-07-01. Heights of Ceresa and Gross-Schoen cycles. https://arxiv.org/abs/2407.01304

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