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Stable principal bundles and reduction of structure group | | Indranil Biswas
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23 Aug 2006 | | Subject: | Algebraic Geometry; Differential Geometry | | Abstract: | Let $E_G$ be a stable principal $G$--bundle over a compact connected Kaehler manifold, where $G$ is a connected reductive linear algebraic group defined over the complex numbers. Let $Hsubset G$ be a complex reductive subgroup which is not necessarily connected, and let $E_Hsubset E_G$ be a holomorphic reduction of structure group. We prove that $E_H$ is preserved by the Einstein-Hermitian connection on $E_G$. Using this we show that if $E_H$ is a minimal reductive reduction in the sense that there is no complex reductive proper subgroup of $H$ to which $E_H$ admits a holomorphic reduction of structure group, then $E_H$ is unique in the following sense: For any other minimal reductive reduction $(H’, E_{H’})$ of $E_G$, there is some element $g$ of $G$ such that $H’= g^{-1}Hg$ and $E_{H’}= E_Hg$. As an application, we give an affirmative answer to a question of Balaji and Koll’ar. | | Source: | arXiv, math/0608569 | | Services: | Forum | Review | PDF | Favorites | |
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