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K-stability and deformations of complex structures

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If you have a question about this talk, please contact Dhruv Ranganathan.

A famous conjecture in complex geometry predicts that the existence of Kaehler metrics with special curvature properties on a projective manifold can be characterized by an algebro-geometric stability notion, K-stability. In this talk, we generalize this picture by taking into account the additional data of a first order deformation of the manifold, which plays the role of a Higgs field for the category of Kaehler manifolds. We will then prove a version of the appropriately generalized stability conjecture in the context of toric manifolds.

This talk is part of the Algebraic Geometry Seminar series.

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