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

Abstract: The Yau-Tian-Donaldson (YTD) conjecture predicts that the existence of an extremal metric (in the sense of Calabi) in a given Kahler class of Kahler manifold is equivalent to a certain algebro-geometric notion of stability of this class. In this talk, we will discuss the resolution of this conjecture for a certain class of toric fibrations, called semisimple principal toric fibrations. After an introduction to the Calabi Problem for general Kahler manifolds, we will focus on the toric setting. Then we will see how to reduce the Calabi problem on the total space of a semisimple principal toric fibration to a weighted constant scalar curvature K\"ahler problem on the toric fibers. If the time allows, I will give elements of proof.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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