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arXiv · 0707.2621

Higher Energies in Kahler Geometry I

Sean Timothy Paul
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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\leq l\leq 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 $l\geq 2$ $F_{\om,l}(\vp)$ 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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Sean Timothy Paul. 2007-07-18. Higher Energies in Kahler Geometry I. https://arxiv.org/abs/0707.2621

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