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arXiv · 2511.12509

Nef cone and successive minima: an example

Ruoyi Guo·Xinyi Yuan
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Abstract

In this paper, we compute the nef cone and the pseudo-effective cone of $C\times J$ for a smooth projective curve $C$ and its Jacobian variety $J$ such that $C\times J$ has the minimal Picard number. As a consequence, we also compute the successive minima of a height function for the relative setting $C\times J\to J$, and our result shows that Zhang's theorem of successive minima does not hold in this case.

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Ruoyi Guo, Xinyi Yuan. 2025-11-16. Nef cone and successive minima: an example. https://arxiv.org/abs/2511.12509

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