An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds. II. (English) Zbl 1209.53032
Summary: Recently, Donaldson proved asymptotic stability for a polarized algebraic manifold \(M\) with polarization class admitting a Kähler 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 Kähler metric, even when \(H\) is not semisimple.
MSC:
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 14L24 | Geometric invariant theory |
| 32Q15 | Kähler manifolds |
| 32Q20 | Kähler-Einstein manifolds |
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
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