2023/09/05 by Michael Hallam, Hallam, Michael
Mathematics · #32Q26 (Secondary) #53C55 (Primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2309.02279
openalex publication_date 2023/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous paper, we showed that the blowup of a weighted extremal Kähler manifold at a relatively stable fixed point admits a weighted extremal metric. Using this result, we prove that a weighted extremal manifold is relatively weighted K-polystable. In particular, a weighted cscK manifold is weighted K-polystable. This strengthens both the weighted K-semistability proved by Lahdili and Inoue, and the weighted K-polystability with respect to smooth degenerations by Apostolov--Jubert--Lahdili, allowing for possibly singular degenerations.