论文标题
Grothendieck在Riemann Sphere上的线束分类
Grothendieck's Classification of Line Bundles over the Riemann Sphere
论文作者
论文摘要
在本文中，我们探讨了Grothendieck在复杂的投影线上对全体形态束进行分类的工作。该纸分为$ 4 $零件。第一部分和第二部分我们建立了必要的背景，以讨论矢量束，滑轮，共同体学等。$ 3^{rd} $章节的主要结果是对复杂的投影线上的Holomorphic Vector Bundles的分类。在$ 4^{th} $章中，我们介绍了主要的$ g $捆绑以及其背后的一些理论，并通过证明Grothendieck的定理完全普遍地结束。目标是（大部分）（主要是）独立的证据证明了Grothendieck的结果可用于采取差异几何形状的人。
In this paper we look at Grothendieck's work on classifying holomorphic bundles over the complex projective line. The paper is divided into $4$ parts. The first and second part we build up the necessary background to talk about vector bundles, sheaves, cohomology, etc. The main result of the $3^{rd}$ chapter is the classification of holomorphic vector bundles over the complex projective line. In the $4^{th}$ chapter we introduce principal $G$-bundles and some of the theory behind them and finish off by proving Grothendieck's theorem in full generality. The goal is a (mostly) self-contained proof of Grothendieck's result accessible to someone who has taken differential geometry.
