English

Hilbert-Samuel formula and positivity over adelic curves

Algebraic Geometry 2022-07-06 v1 Number Theory

Abstract

We establish, in the setting of Arakelov geometry over adelic curves, an arithmetic Hilbert-Samuel theorem describing the asymptotic behaviour of the metrized graded linear series of an adelic line bundle in terms of its arithmetic intersection number. We then study positivity conditions of adelic line bundles.

Keywords

Cite

@article{arxiv.2207.02033,
  title  = {Hilbert-Samuel formula and positivity over adelic curves},
  author = {Huayi Chen and Atsushi Moriwaki},
  journal= {arXiv preprint arXiv:2207.02033},
  year   = {2022}
}
R2 v1 2026-06-24T12:14:29.606Z