Nef cone and successive minima: an example

2025/11/16 by Guo, Ruoyi, Yuan, Xinyi · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Tensor decomposition and applications #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2511.12509

Abstract

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

Citations

• Adelic line bundles on quasi-projective varieties
• Gross--Schoen Cycles and Dualising Sheaves
• Equidistribution over function fields
• Hyperelliptic jacobians without complex multiplication
• Arithmetic height functions over finitely generated fields

Cited by

• A quantitative dynamical Zhang fundamental inequality and Bogomolov-type problems

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