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/10.1007/9783319250403_32
Video: http://www.youtube.com/watch?v=7FfYJ94VhAk
Slides: Philippon_Heights of toric.pdf
Presentation: https://www.see.asso.fr/node/14286
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
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.