2018/03/19 by Akito Futaki, Futaki, Akito, Hajime Ono +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1803.06801
openalex publication_date 2018/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this expository paper we review on the existence problem of Einstein-Maxwell Kähler metrics, and make several remarks. Firstly, we consider a slightly more general set-up than Einstein-Maxwell Kähler metrics, and give extensions of volume minimization principle, the notion of toric K-stability and other related results to the general set-up. Secondly, we consider the toric case when the manifold is the one point blow-up of the complex project plane and the Kähler class Ω is chosen so that the area of the exceptional curve is sufficiently close to the area of the rational curve of self-intersection number 1. We observe by numerical analysis that there should be a Killing vector field K which gives a toric K-stable pair (Ω, K) in the sense of Apostolov-Maschler.