English

On an arithmetic inequality on $\mathbb{P}^1_{\mathbb{Q}}$

Algebraic Geometry 2014-12-09 v1 Number Theory

Abstract

We establish an inequality comparing the height and the χ\chi-arithmetic volume of toric metrized divisors on PQ1\mathbb{P}^1_{\mathbb{Q}}. This gives a partial answer to a question of Burgos, Moriwaki, Philippon and Sombra ([5, remark 5.13]).

Keywords

Cite

@article{arxiv.1409.6181,
  title  = {On an arithmetic inequality on $\mathbb{P}^1_{\mathbb{Q}}$},
  author = {Mounir Hajli},
  journal= {arXiv preprint arXiv:1409.6181},
  year   = {2014}
}

Comments

Accepted for publication in IJNT

R2 v1 2026-06-22T06:02:24.183Z