The Futaki invariant and the Mabuchi energy of a complete intersection

Details The Futaki invariant and the Mabuchi energy of a complete intersection The Futaki invariant and the Mabuchi energy of a complete intersection

2003-12-31

arxiv.org/abs/math/0312529v1

Comm. in Analysis and Geometry (2004) 12, 323-345

Mathematics

Differential Geometry

21 pages

Scientific paper

We study the Futaki invariant and the Mabuchi K-energy of a K\"ahler 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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