An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, II

Details An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, II An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, II

2004-10-09

arxiv.org/abs/math/0410239v1

Mathematics

Differential Geometry

Submitted to J. Differential Geom. in 2003. Revised in May, 2004

Scientific paper

10.1007/s00222-004-0387-y

Recently, Donaldson proved asymptotic stability for a polarized algebraic manifold $M$ with polarization class admitting a K\"ahler metric of constant scalar curvature, essentially when the linear algebraic part $H$ of $Aut^0(M)$ is semisimple. The purpose of this paper is to give a generalization of Donaldson's result to the case where the polarization class admits an extremal K\"ahler metric, even when $H$ is not semisimple.

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