关于Barth-Van de Ven-Tyurin-Sato定理
On the Barth-Van de Ven-Tyurin-Sato theorem
摘要：
Barth-Van de Ven-Tyurin-Sato定理证明了无限复射影空间$\mathbf{P}^\infty$上的有限秩向量丛同构于线丛的直和。我们建立了局部完备线性指数簇$\mathbf{X}$上的充分条件，保证了相同的结果在$\mathbf{X}$上成立.然后，我们表现出自然类的局部完全线性ind-簇，满足这些充分条件。关键词：指数簇，向量丛
英文摘要：
The Barth-Van de Ven-Tyurin-Sato Theorem claims that any finite rank vector bundle on the infinite complex projective space $\mathbf{P}^\infty$ is isomorphic to a direct sum of line bundles. We establish sufficient conditions on a locally complete linear ind-variety $\mathbf{X}$ which ensure that the same result holds on $\mathbf{X}$. We then exhibit natural classes of locally complete linear ind-varieties which satisfy these sufficient conditions. Keywords: ind-variety, vector bundle
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