Arithmetic positivity on toric varieties
Abstract
We continue with our study of the arithmetic geometry of toric varieties. In this text, we study the positivity properties of metrized R-divisors in the toric setting. For a toric metrized R-divisor, we give formulae for its arithmetic volume and its chi-arithmetic volume, and we characterize when it is arithmetically ample, nef, big or pseudo-effective, in terms of combinatorial data. As an application, we prove a Dirichlet's unit theorem on toric varieties, we give a characterization for the existence of a Zariski decomposition of a toric metrized R-divisor, and we prove a toric arithmetic Fujita approximation theorem.
Keywords
Cite
@article{arxiv.1210.7692,
title = {Arithmetic positivity on toric varieties},
author = {Jose Ignacio Burgos Gil and Atsushi Moriwaki and Patrice Philippon and Martin Sombra},
journal= {arXiv preprint arXiv:1210.7692},
year = {2022}
}
Comments
54 pages, published in Journal of Algebraic Geometry 25 (2016) 201-272. The present version corrects a mistake in the published version of Corollary 6.2