I. B. Penkov, A. S. Tikhomirov, “Triviality of vector bundles on twisted ind-Grassmannians”, Mat. Sb., 2011, Volume 202, Number 1,Pages <nobr>65

This article is cited in 5 papers

Triviality of vector bundles on twisted ind-Grassmannians

I. B. Penkov^a, A. S. Tikhomirov^b

^a School of Engineering and Science, Jacobs University Bremen, Germany
^b Yaroslavl State Pedagogical University named after K. D. Ushinsky

Abstract: Twisted ind-Grassmannians are ind-varieties $\mathbf G$ obtained as direct limits of Grassmannians $G(i_m,V^{n_m})$ for $m\in\mathbb Z_{>0}$ under embeddings of degree greater than $1$. It has been conjectured by Donin and Penkov (2003) that any vector bundle of finite rank on a twisted ind-Grassmannian is trivial. We prove this conjecture.
Bibliography: 16 titles.

Keywords: ind-variety, twisted ind-Grassmannian, vector bundle.

UDC: 512.723

MSC: 14M15, 14J60

Received: 08.07.2009 and 19.07.2010

DOI: 10.4213/sm7599