Weighted canonical Kähler metrics: stability and existence through blowups

Michael Hallam (Aarhus University)

Monday 13th November, 2023 16:00-17:00 Maths 311B

Abstract

A motivating question in the field of Kähler geometry is whether a given Kähler manifold admits a canonical Kähler metric. Conjecturally, a Kähler manifold admits a canonical, or "best" Kähler metric, if and only if it satisfies a suitable algebro-geometric stability notion, called K-stability. In this talk I will give a brief introduction to the setting, before explaining how this has been vastly generalised to "weighted" canonical Kähler metrics, which recover many interesting geoemtric situations. I will then discuss new work which shows how stability may be proven using an existence result for weighted canonical Kähler metrics on blowups.

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