Nef cone and successive minima: an example
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911456402866176 |
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| author | Guo, Ruoyi Yuan, Xinyi |
| author_facet | Guo, Ruoyi Yuan, Xinyi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nef cone and successive minima: an example Guo, Ruoyi Yuan, Xinyi Algebraic Geometry Number Theory 14C20, 14G40, 14H40 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. |
| title | Nef cone and successive minima: an example |
| topic | Algebraic Geometry Number Theory 14C20, 14G40, 14H40 |
| url | https://arxiv.org/abs/2511.12509 |