Arakelov heights in toric varieties
Algebra and Geometry Seminar
13th February 2019, 2:30 pm – 3:30 pm
Howard House, 4th Floor Seminar Room
Starting from the classical definition of height given by Northcott and Weil, I will present the main philosophy and guidelines of adelic Arakelov geometry. In the case of toric varieties, I will show how it is possible to translate such a theory in terms of convex geometry, following the work of Burgos Gil, Philippon and Sombra. I will then present a combinatorial formula relating the height of a hypersurface in a toric variety with the collection of the v-adic Ronkin functions of its defining Laurent polynomial. If time permits, I will sketch results and obstacles for a higher codimensional analogue.