2023/04/17 by Michael Hallam, Hallam, Michael
Mathematics · Physics and Astronomy · #53C55 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2304.08338
openalex publication_date 2023/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that if a compact Kähler manifold admits a weighted extremal metric for the action of a torus, so too does its blowup at a relatively stable point that is fixed by both the torus action and the extremal field. This generalises previous results on extremal metrics by Arezzo--Pacard--Singer and Székelyhidi to many other canonical metrics, including extremal Sasaki metrics, deformations of Kähler--Ricci solitons and μ-cscK metrics. In a sequel to this paper, we use this result to study the weighted K-stability of weighted extremal manifolds.