• Corpus ID: 119638299

Arithmetic geometry of toric varieties. metrics, measures and heights

@article{Gil2014ArithmeticGO,
  title={Arithmetic geometry of toric varieties. metrics, measures and heights},
  author={Jos{\'e} I. Burgos Gil and Patrice Philippon and Mart{\'i}n Sombra},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions. To state and prove this result, we study the Arakelov geometry of toric varieties. In particular, we consider models over a discrete valuation ring, metrized line bundles, and their associated measures and heights. We show that these notions can be translated in terms of convex analysis, and are closely related… 

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