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The Heat Equation Approach to Hermitian-Einstein Metrics on Stable Bundles

  • Yum-Tong Siu
Part of the DMV Seminar book series (OWS, volume 8)

Abstract

In this chapter we discuss here the problem of the existence of Hermitian-Einstein metrics on stable bundles. The case of stable bundles over compact complex curves was done by Narasimhan and Seshadri [N-S] and alternative proof later given by Donaldson [D1]. Donaldson [D2] treated the case of stable bundles over compact algebraic surfaces by using the heat equation method. Recently a paper of Uhlenbeck and Yau [U-Y] dealt with the problem for stable bundles over a compact Kahler manifold by using the continuity method. A recent preprint of N. P. Buchdahl [Bu] considered the case of stable bundles over compact complex surfaces that admit a ∂†̄-closed positive definite (1.1)-form. A most recent preprint of Donaldson [D3] carried over his treatment of the surface case to higher dimension. Simpson [Si] in his Harvard University dissertation under the direction of W. Schmid proved the existence of Hermitian-Einstein metrics for stable systems of Hodge bundles without the restriction of algebraicity.

Keywords

Vector Bundle Line Bundle Curvature Tensor Holomorphic Vector Bundle Ample Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel 1987

Authors and Affiliations

  • Yum-Tong Siu
    • 1
  1. 1.Department of Mathematics Science CenterHarvard UniversityCambridgeUSA

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