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摘要翻译：
本文证明了经典Narasimhan-Seshadri定理在高维上的一个类似定理，证明了在光滑射影簇$x$上强稳定的0次向量丛具有固定的充足线丛$theta$。作为应用，在特征零点域上，我们对Balaji和Koll\'ar最近一篇论文中的主要定理给出了一个新的证明，并导出了该定理的一个有效版本；在具有正特征的不可数域上，如果$G$是单连通代数群，且域的特征大于$G$的Coxeter指数，我们证明了光滑射影曲面上强稳定主$G$丛的存在性，其完整群是$G$的整。
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英文标题：
《An analogue of the Narasimhan-Seshadri theorem and some applications》
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作者：
V. Balaji and A.J. Parameswaran
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最新提交年份：
2010
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
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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PDF链接：
https://arxiv.org/pdf/0809.3765
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