Families of singular Kähler-Einstein metrics

Abstract: I will outline the main results and ideas from a recent joint work with E. Di Nezza and V. Guedj. The general theme is as follows: let p:X\to Y be a holomorphic, proper surjective map from a complex Kähler space X and assume that the fibers X_y admit some (possibly twisted) singular Kähler-Einstein metric. We show that the potentials of these metrics admit uniform bounds when y varies in compact subsets. If time permits, I will mention a connection with an earlier work (joint with J. Cao and M. Paun) on the psh variation of the Kähler-Einstein metric on families of manifolds of general type.

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

Audience: researchers in the topic

( paper )

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CRM - Séminaire du CIRGET / Géométrie et Topologie

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