Principle bundles admitting a holomorphic structure

Details Principle bundles admitting a holomorphic structure Principle bundles admitting a holomorphic structure

1996-01-18

arxiv.org/abs/alg-geom/9601019v1

Mathematics

Algebraic Geometry

AMSLatex

Scientific paper

Let $M$ be a compact connected K\"ahler 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 $\deg (T/{\E}_{l-1}) \geq 0$, then a holomorphic principal $G$-bundle $P$ on $M$ admitting a compatible holomorphic connection is semistable. Moreover, if $\deg (T/{\E}_{l-1}) >0$, then such a bundle $P$ actually admits a compatible flat $G$-connection.

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