Stable principal bundles and reduction of structure group
| dc.creator | Biswas, Indranil | |
| dc.date | 2006-08-23 | |
| dc.date.accessioned | 2026-07-07T07:22:04Z | |
| dc.date.available | 2026-07-07T07:22:04Z | |
| dc.description | 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 $H\subset G$ be a complex reductive subgroup which is not necessarily connected, and let $E_H\subset E_G$ 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 Kollár. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608569 | |
| dc.identifier | http://arxiv.org/abs/math/0608569 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115527 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.title | Stable principal bundles and reduction of structure group | |
| dc.type | text |