2002/03/24 by D. H. Phong, Phong, D. H., Jacob Sturm +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.math/0203254
PlainTEX file, 28 pages
arxiv created 2002/03/24 · openalex publication_date 2002/03/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An explicit seminorm ||f||# on the vector space of Chow vectors of projective varieties is introduced, and shown to be a generalized Mabuchi energy functional for Chow varieties. The singularities of the Chow varieties give rise to currents supported on their singular loci, while the regular parts are shown to reproduce the Mabuchi energy functional of the corresponding projective variety. Thus the boundedness from below of the Mabuchi functional, and hence the existence of Kähler-Einstein metrics, is related to the behavior of the current [Ys] and the seminorm ||f||# along the orbits of SL(N+1,\bf C).