2025/06/12 by Frey, Gabriel
Mathematics · #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.2506.10679
openalex publication_date 2025/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an equivariant version of the CM minimization conjecture for extremal Kähler manifolds. This involves proving that, given an equivariant punctured family of polarized varieties, a relative version of the CM degree is strictly minimized by an extremal filling. This generalizes a result by Hattori for cscK manifolds with discrete automorphism group by allowing automorphisms and extremal metrics. As a main tool, we extend results by Székelyhidi on asymptotic filtration Chow stability of cscK manifolds with discrete automorphism group to the extremal setting.