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Einstein-Hermitian connections on polystable principal bundles over a compact Kähler manifold

From: American Journal of Mathematics
Volume 123, Number 2, April 2001
pp. 207-228 | 10.1353/ajm.2001.0007

Abstract

Abstract:

Given a compact Kähler manifold M and a connected reductive algebraic group G over [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], a prinlcipal G-bundle over M admits an Einstein-Hermitian connection if and only if the principal bundle is polystable. If M is a projective manifold, a Higgs G-bundle over M admits an Einstein-Hermitian connection if and only if the Higgs bundle is polystable.