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arXiv · 0706.3912

Triviality of vector bundles on sufficiently twisted ind-Grassmannians

Ivan Penkov·Alexander S. Tikhomirov
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Abstract

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 $ϕ_m:G(r_m,V^{r_m})\to G(r_{m+1}, V^{r_{m+1}})$ 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 $\lim_{m\to\infty}\frac{r_m}{°ϕ_1...\degϕ_m}=0$.

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Ivan Penkov, Alexander S. Tikhomirov. 2007-06-27. Triviality of vector bundles on sufficiently twisted ind-Grassmannians. https://arxiv.org/abs/0706.3912

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