A Yau-Tian-Donaldson correspondence on a class of toric fibrations

Abstract: 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).

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

[[Please provide your first and last name so that the speaker can identify you. Kindly submit your questions or comments using the chat box, not via audio.]]

The livestream is on Zoom at uqam.zoom.us/j/88383789249 It is recommended to subscribe to the CIRGET newsletter. Please send an email to haedrich.alexandra@uqam.ca , providing your name and affiliation.

Some talks can be seen at www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA