Scalar curvature and deformations of complex structures

Abstract: A classical problem in Kähler geometry is to choose, among all the possible Kähler metrics on a manifold, a canonical representative of each Kähler class. This is usually done by imposing curvature conditions on the metric, such as Ricci-flat, Kähler-Einstein, or constant scalar curvature. In this talk, I will describe how the problem changes when we also consider deformations of the complex structure, introducing a partial differential equation which gives a canonical choice of a Kähler metric for each deformation class. Time permitting, I will examine the case of toric manifolds in more detail. The talk is based on arxiv:2202.00429 and joint work with J. Stoppa.

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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The recorded talks can be found at CIRGET channel : www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA