Higher Energies in Kahler Geometry I

2007/07/18 by Sean Timothy Paul, Paul, Sean Timothy
Mathematics · #53C55 #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.0707.2621

openalex publication_date 2007/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X\hookrightarrow \cpn be a smooth complex projective variety of dimension n. Let λ be an algebraic one parameter subgroup of G:=\gc. Let 0≤ l≤ n+1. We associate to the coefficients F_l(λ) of the normalized weight of λ on the mth Hilbert point of X new energies F_\om,l(\vp). The (logarithmic) asymptotics of F_\om,l(\vp) along the potential deduced from λ is the weight F_l(λ). F_\om,l(\vp) reduces to the Aubin energy when l=0 and the K-Energy map of Mabuchi when l=1. When l≥ 2 F_\om,l(\vp) coincides (modulo lower order terms) with the functional E_\om,l-1(\vp) introduced by X.X. Chen and G.Tian.

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