Osaka Journal of Mathematics

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

Toshiki Mabuchi

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Abstract

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 $\operatorname{Aut}^{0}(M)$ 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.

Article information

Source
Osaka J. Math., Volume 46, Number 1 (2009), 115-139.

Dates
First available in Project Euclid: 25 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1235574041

Mathematical Reviews number (MathSciNet)
MR2531143

Zentralblatt MATH identifier
1209.53032

Subjects
Primary: 14L24: Geometric invariant theory [See also 13A50] 32Q15: Kähler manifolds
Secondary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx] 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Citation

Mabuchi, Toshiki. An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, II. Osaka J. Math. 46 (2009), no. 1, 115--139. https://projecteuclid.org/euclid.ojm/1235574041


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