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) Chung-Min Pan - Université Paul Sabatier,
Titre Canonical metrics and pluripotential theory along degenerate families
Horaire14:00 à 15:00

Searching for canonical metrics in Kähler classes has been a central theme in Kähler geometry for decades. This talk aims to explain a method for studying singular canonical metrics in families of singular varieties with a relative pluripotential theory and a variational approach in families. The main focus of the talk will be the singular Kähler-Einstein (KE) metrics on families of Fano varieties. Following a brief review of singular KE metrics and a variational method, I will introduce a notion of convergence of quasi-plurisubharmonic functions in families. Several classical properties will be extended under this framework. Then, I will present an Euclidien openness result of the existence of KE metrics via an analytic method and how to establish uniform a priori estimates in families. If time permits, we will conclude by exploring the potential development of this method to study singular cscK metrics.