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摘要翻译：
Twisted ind-Grassmannians是Grassmannians$G(r_m,V^{r_m}）$的直接极限，对于$M\in\zz_{>0}$,在嵌入$\phi_m:G(r_m,V^{r_m}）\到G(r_{m+1},V^{r_{m+1}}）$下得到的ind-变种$\gg$。本文在{PT}和{DP}中猜想，在一个扭曲的ind-Grassmannian上，任何有限秩的向量丛都是平凡的。我们在ind-Grassmannian$\gg$充分扭曲的假设下证明了这个猜想，即$\lim_{m\to\infty}\frac{r_m}{\deg\phi_1…\deg\phi_m}=0$。
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英文标题：
《Triviality of vector bundles on sufficiently twisted ind-Grassmannians》
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作者：
Ivan Penkov, Alexander S. Tikhomirov
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最新提交年份：
2007
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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：
Twisted ind-Grassmannians are ind-varieties $\GG$ obtained as direct limits of Grassmannians $G(r_m,V^{r_m})$, for $m\in\ZZ_{>0}$, under embeddings $\phi_m:G(r_m,V^{r_m})\to G(r_{m+1}, V^{r_{m+1}})$ of degree greater than one. It has been conjectured in \cite{PT} and \cite{DP} that any vector bundle of finite rank on a twisted ind-Grassmannian is trivial. We prove this conjecture under the assumption that the ind-Grassmannian $\GG$ is sufficiently twisted, i.e. that $\lim_{m\to\infty}\frac{r_m}{\deg \phi_1...\deg\phi_m}=0$.
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PDF链接：
https://arxiv.org/pdf/0706.3912
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