Principle bundles admitting a holomorphic structure

1996/01/18 by Indranil Biswas, Biswas, Indranil
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9601019

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arxiv created 1996/01/18 · arxiv updated 2009/11/30

Abstract

Let M be a compact connected Kähler manifold and let \E_l-1 be the smallest term in the Harder-Narasimhan filtration of its tangent bundle. Let G be an affine algebraic reductive group over \C. We prove the following result: If M satisfies the condition that °(T/\E_l-1) ≥ 0, then a holomorphic principal G-bundle P on M admitting a compatible holomorphic connection is semistable. Moreover, if °(T/\E_l-1) >0, then such a bundle P actually admits a compatible flat G-connection.

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