Kähler Quantization in Degenerate Setting

Abstract: Kähler quantization provides a bridge between infinite-dimensional geometric objects in Kähler geometry and finite-dimensional data arising from spaces of holomorphic sections. In this talk, I will first review this correspondence in the ample case, where it is well understood and plays a central role in the study of canonical metrics. I will then explain how this picture can be extended beyond the ample setting, where smooth positively curved metrics are no longer available. In particular, I will describe how the Monge–Ampère energy can still be recovered from finite-dimensional approximations in the semipositive and big setting. Finally, if time permits, I will outline the idea of the proof.

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

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