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The Futaki invariant and the Mabuchi energy of a complete intersection

D. H. Phong·Jacob Sturm
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Abstract

We study the Futaki invariant and the Mabuchi K-energy of a Kähler manifold $M$ using the Deligne pairing technique developed in earlier papers. We first prove a rather simple characterization of the Futaki character: The Futaki character on a Q-Fano variety is the eigenvalue of the action of $Aut(M)$ on $Chow(M)$, the Chow point of $M$. We use this to give a new proof of Lu's theorem on the Futaki invariant of a complete intersection. In the last theorem, we prove a non-linear generalization of Lu's formula which expresses the K-energy of a smooth complete intersection as a singular norm on the space of defining polynomials.

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D. H. Phong, Jacob Sturm. 2003-12-31. The Futaki invariant and the Mabuchi energy of a complete intersection. https://arxiv.org/abs/math/0312529

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