ar X iv : m at h / 06 06 50 5 v 3 [ m at h . D G ] 1 9 A pr 2 00 8 CM STABILITY AND THE GENERALIZED FUTAKI INVARIANT II SEAN
نویسنده
چکیده
The Mabuchi K-energy map is exhibited as a singular metric on the refined CM polarization of any equivariant family X p → 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.
منابع مشابه
ar X iv : m at h / 06 06 50 5 v 4 [ m at h . D G ] 2 3 A pr 2 00 8 CM STABILITY AND THE GENERALIZED FUTAKI INVARIANT II
The Mabuchi K-energy map is exhibited as a singular metric on the refined CM polarization of any equivariant family X p → 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.
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