Einstein type metrics and stability on vector bundles

Conan Leung Chinese Univ of HK

Computational Geometry mathscidoc:1608.09015

Journal of Differential Geometry, 45, 514-546, 1997
In this paper we show that stability for holomorphic vector bundles are equivalent to the existence of solutions to certain system of Monge Ampere equations parametrized by a parameter k. We solve this fully nonlinear elliptic system by singular perturbation technique and show that the vanishing of obstructions for the perturbation is given precisely by the stability condition. This can be interpreted as an infinite dimensional analog of the equivalencybetween Geometric Invariant Theory and Symplectic Reduction for moduli space of vector bundles.
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@inproceedings{conan1997einstein,
  title={Einstein type metrics and stability on vector bundles},
  author={Conan Leung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831171534601208590},
  booktitle={Journal of Differential Geometry},
  volume={45},
  pages={514-546},
  year={1997},
}
Conan Leung. Einstein type metrics and stability on vector bundles. 1997. Vol. 45. In Journal of Differential Geometry. pp.514-546. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831171534601208590.
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