The Sign of Scalar Curvature on Kähler Blowups

The HADES seminar on Tuesday, April 2nd, will be at 3:30pm in Room 939.

Speaker: Garrett Brown

Abstract: Blowing up is a construction in complex geometry that can be thought of as the analog to connected sum in smooth topology. In this talk we will show that the property of having a positive (or negative) scalar curvature Kähler metric is preserved under blowing up points on a compact complex manifold of any dimension. This is done by solving a certain prescribed scalar curvature equation. The most crucial step is establishing uniform estimates for the linearized scalar curvature operators of a family of metrics on the blowup, for which the underlying geometry plays an interesting role. In the case of positive scalar curvature in two complex dimensions, this answers a question of Hitchin and Lebrun in the affirmative and completes the classification of positive scalar curvature Kähler surfaces.

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