2021/10/06 by Takahiro Aoi, Yoshinori Hashimoto, Aoi, Takahiro +3
Mathematics · #32Q26 (Secondary) #53C55 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2110.02518
openalex publication_date 2021/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the existence of constant scalar curvature Kähler metrics with cone singularities along a divisor implies log K-polystability and G-uniform log K-stability, where G is the automorphism group which preserves the divisor. We also show that a constant scalar curvature Kähler cone metric along an ample divisor of sufficiently large degree always exists. We further show several properties of the path of constant scalar curvature Kähler cone metrics and discuss uniform log K-stability of normal varieties.