Ana Maria Botero
Ana Maria Botero
On the arithmetic geometry of toric varieties: old and new
Abstract: We give an overview of the arithmetic geometry of toric varieties developed by J. Burgos, P. Philippon and M. Sombra in 2014. In particular we discuss the classification of continuous toric metrics on toric line bundles both in the Archimedean and in the non-Archimedean case. Then we report on partial results generalizing this classification for toric metrics on toric vector bundles using the theory of buildings. This is joint work in progress with J. Burgos, K. Kaveh and V. Mallik.