Height of toric varieties

Mardi 17 mars 2009 16:00-17:00 - José Ignacio Burgos Gil - Université de Barcelone

Résumé : To a toric variety provided with an ample line bundle we can associate a polytope. Much of the algebraic geometry of the algebraic variety and the line bundle can be read from the polytope. For instance the degree is determined by the volume of the polytope. The pourpose of this talk is to show the analogue in Arakelov geometry of this result. Namely, that the height of a toric variety is determined by the integral along the polytope of the Legendre dual of the logarithm of the norm of a section. We will see how this result allows us to compute explicitly the height of many toric varieties and we will also discuss the adelic version of this result. This is joint work with P.Philippon and M.Sombra.

Lieu : bât. 425 - 113-115

Height of toric varieties  Version PDF