Séminaires GAT à venir
Séminaires les jeudi à 14h en salle BC101.
Organisé par Lucien Hennecart et Jacques Darné.
Fano varieties are among the fundamental building blocks of algebraic varieties, and their investigation is a central question in birational geometry. The Mukai conjecture concerns their geography, predicting a relationship between the Picard rank and the divisibility of the anti-canonical divisor.
In this talk, I will present a proof of the Mukai conjecture for spherical varieties, a large class of normal varieties with a group action that generalises toric, flag, and symmetric varieties. Our approach combines two strategies: the study of rational curves on Fano varieties and decomposability properties of the anti-canonical divisor. This allows us to connect the spherical Mukai conjecture to a geometric characterisation of toric varieties via log-canonical pairs conjectured by Shokurov. The latter is a key step in our proof, reducing one part of the question to the toric case, which was proven by Casagrande.
This is joint work with Giuliano Gagliardi and Heath Pearson. No prior knowledge of spherical varieties will be assumed.
https://indico.math.cnrs.fr/event/16184/overview