Relative uniform Yau-Tian-Donaldson correspondence for projective bundles over a curve

Abstract: In this talk, I will present recent joint work with Simon Jubert on a version of the Yau–Tian–Donaldson correspondence for projective bundles Y=P(E) over a curve. By earlier work of Apostolov–Keller, if a Kähler class on Y admits an extremal Kähler metric, then E must split as a direct sum of stable vector bundles. We show that, for such E, a Kähler class on Y admits an extremal Kähler metric if and only if it is relatively uniformly K-stable. The proof uses a distinguished family of test configurations, called compatible test configurations, constructed from the horospherical symmetry of the fibers, together with the framework of weighted constant scalar curvature Kähler metrics.

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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