Heights of toric varieties, integration over polytopes and entropy - José Ignacio Burgos Gil, Martin Sombra, Patrice Philippon
Author(s): José Ignacio Burgos Gil, Martin Sombra, Patrice Philippon
DOI URL: http://dx.doi.org/10.1007/978-3-319-25040-3_32
Slides: Philippon_Heights of toric.pdf
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We present a dictionary between arithmetic geometry of toric varieties and convex analysis. This correspondence allows for effective computations of arithmetic invariants of these varieties. In particular, combined with a closed formula for the integration of a class of functions over polytopes, it gives a number of new values for the height (arithmetic analog of the degree) of toric varieties, with respect to interesting metrics arising from polytopes. In some cases these heights are interpreted as the average entropy of a family of random processes.