An analogue of the Narasimhan-Seshadri theorem and some applications

Details An analogue of the Narasimhan-Seshadri theorem and some applications An analogue of the Narasimhan-Seshadri theorem and some applications

2008-09-22

arxiv.org/abs/0809.3765v3

Mathematics

Algebraic Geometry

42 pages. Theorem 3 of this version is new. Typos have been corrected. To appear in Journal of Topology

Scientific paper

We prove an analogue in higher dimensions of the classical Narasimhan-Seshadri theorem for strongly stable vector bundles of degree 0 on a smooth projective variety $X$ with a fixed ample line bundle $\Theta$. As applications, over fields of characteristic zero, we give a new proof of the main theorem in a recent paper of Balaji and Koll\'ar and derive an effective version of this theorem; over uncountable fields of positive characteristics, if $G$ is a simple and simply connected algebraic group and the characteristic of the field is bigger than the Coxeter index of $G$, we prove the existence of strongly stable principal $G$ bundles on smooth projective surfaces whose holonomy group is the whole of $G$.

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