English

Nef cone and successive minima: an example

Algebraic Geometry 2026-02-20 v2 Number Theory

Abstract

In this paper, we compute the nef cone and the pseudo-effective cone of C×JC\times J for a smooth projective curve CC and its Jacobian variety JJ such that C×JC\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×JJC\times J\to J, and our result shows that Zhang's theorem of successive minima does not hold in this case.

Cite

@article{arxiv.2511.12509,
  title  = {Nef cone and successive minima: an example},
  author = {Ruoyi Guo and Xinyi Yuan},
  journal= {arXiv preprint arXiv:2511.12509},
  year   = {2026}
}
R2 v1 2026-07-01T07:39:36.839Z