mu-cscK metrics and muK-stability of polarized manifolds

Abstract: I will talk about a framework unifying both the frameworks on "cscK metrics and K-stability of polarized manifolds" and "Kahler-Ricci solitons and modified K-stability of Fano manifolds". There are two divided contents as follows.

1. Formulation of mu-cscK metrics and brief remarks on results parallel to the usual canonical metrics. On some attractive special features/phenomenon of mu-cscK metrics; "extremal limit" and "phase transition". On a little examples.

2. How to formulate/derive/express mu-Futaki invariant of test configurations with general singularities. On a counterpart of CM line bundle for muK-stability.

If time permits, I will also propose future problems/projects and its applications, especially towards the algebraic moduli problems of Fano varieties admitting Kahler-Ricci solitons.

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

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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