Positive Scalar Curvature Kähler (pscK) Surfaces

Garrett M. Brown

UC Berkeley

I am a fourth year math PhD student at UC Berkeley working with Song Sun, who recently moved to the IASM at Zhejiang University. My interests lie in differential geometry / geometric analysis, usually in the setting of complex geometry. From Fall 2017 to Spring 2021, I was an undergraduate at Harvard College. Before that, I resided in southeast Michigan.

I am grateful for the support of an NSF Graduate Research Fellowship.

# Time

Wednesday, 10:30-11:30 am

April 9, 2025

# Venue

B725, Shuangqing Complex Building

#Abstract

The interaction between curvature and algebraic geometry is a guiding principle in Kähler geometry. For example, it is a result of Yau that a Kähler manifold with positive average scalar curvature has negative Kodaira dimension, and that minimal surfaces in this class admit pscK metrics. It was conjectured by Lebrun that all negative Kodaira dimension surfaces should admit pscK metrics. In this talk, I will explain a recent resolution to this conjecture by showing one can actually make the scalar curvature on the blowup of any Kähler manifold C^0 close to that of any starting Kähler metric on the base.