Séminaires : Séminaire d'Analyse et Géométrie

Equipe(s) :
Responsables :O. Biquard, A. Deruelle, E. Di Nezza, I. Itenberg, X. Ma
Email des responsables : {olivier.biquard, alix.deruelle, eleonora.dinezza, ilia.itenberg, xiaonan.ma}@imj-prg.fr
Salle : 15–25.502
Adresse :Jussieu

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Orateur(s) Simon Jubert - IMJ-PRG,
Titre Yau–Tian–Donaldson correspondence on a class of toric fibrations
Horaire14:00 à 15:00

The Yau–Tian–Donaldson conjecture predicts that the existence of an extremal metric (in the sense of Calabi) in a given Kähler class of Kähler manifold is equivalent to a certain algebro-geometric notion of stability of this class. In this talk, we will discuss a resolution of this conjecture for a certain type of toric fibrations, called semisimple principal toric fibrations. One of the main assets of these fibrations is that they come equipped with a connection which allows defining, from any Kähler metrics on the toric fiber X, a Kähler metric on the total space Y. After an introduction to the Calabi Problem for general compact Kähler manifolds, we will focus on the weighted toric setting. Then, I will explain how to translate the Calabi problem on Y, to a weighted cscK problem on the corresponding toric fiber X (arxiv paper: arXiv:2108.12297