CM Stability And The Generalized Futaki Invariant II

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The Mabuchi K-energy map is exhibited as a singular metric on the refined CM polarization of any equivariant family $\mathbf{X}\overset{p}{\to} S$. Consequently we show that the generalized Futaki invariant is the leading term in the asymptotics of the reduced K-energy of the generic fiber of the map $p$. Properness of the K-energy implies that the generalized Futaki invariant is strictly negative.
15, fully rewritten, references added

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Differential Geometry, Algebraic Geometry, 53C55 (Primary), 14D06 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/159358

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606505
 http://arxiv.org/abs/math/0606505

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arXiv