Successive minima of toric height functions
Number Theory
2015-09-08 v2 Algebraic Geometry
Abstract
Given a toric metrized R-divisor on a toric variety over a global field, we give a formula for the essential minimum of the associated height function. Under suitable positivity conditions, we also give formulae for all the successive minima. We apply these results to the study, in the toric setting, of the relation between the successive minima and other arithmetic invariants like the height and the arithmetic volume. We also apply our formulae to compute the successive minima for several families of examples, including weighted projective spaces, toric bundles and translates of subtori.
Cite
@article{arxiv.1403.4048,
title = {Successive minima of toric height functions},
author = {Jose Ignacio Burgos Gil and Patrice Philippon and Martin Sombra},
journal= {arXiv preprint arXiv:1403.4048},
year = {2015}
}
Comments
To appear in Annales de l'Institut Fourier (Grenoble), 40 pages, 5 figures