Exponential maps in Kahler geometry

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• David Witt Nystrom (University of Cambridge)
• Wednesday 04 December 2013, 14:15-15:15
• MR 13, CMS.

If you have a question about this talk, please contact Dr. J Ross.

I will discuss some joint work with Julius Ross. We consider a compact complex submanifold Y inside a Kahler manifold X. By proving local regularity for certain solutions to the complex Homogeneous Monge-Ampere equation we construct a canonical exponential map from a neighbourhood of Y in its normal bundle to a neighbourhood of Y in X. This map has some interesting properties relating to the Kahler structure of X which in general are not shared by the more classical exponential map coming from geodeisic flows. On a Riemann surface we have a physical interpretation in terms of the Hele-Shaw flow.

This talk is part of the Algebraic Geometry Seminar series.

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