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arXiv · 1210.7692

Arithmetic positivity on toric varieties

Jose Ignacio Burgos Gil·Atsushi Moriwaki·Patrice Philippon·Martin Sombra
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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.

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Jose Ignacio Burgos Gil, Atsushi Moriwaki, Patrice Philippon, Martin Sombra. 2012-10-29. Arithmetic positivity on toric varieties. https://arxiv.org/abs/1210.7692

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