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Sbornik: Mathematics, 2011, Volume 202, Issue 1, Pages 61–99
DOI: https://doi.org/10.1070/SM2011v202n01ABEH004138 (Mi sm7599) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Triviality of vector bundles on twisted ind-Grassmannians

I. B. Penkova, A. S. Tikhomirovb

a School of Engineering and Science, Jacobs University Bremen, Germany
b Yaroslavl State Pedagogical University named after K. D. Ushinsky
English version PDF (583 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM2011v202n01ABEH004138
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.
Received: 08.07.2009 and 19.07.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 1, Pages 65–104
DOI: https://doi.org/10.4213/sm7599
Bibliographic databases:
Document Type: Article
UDC: 512.723
MSC: 14M15, 14J60
Language: English
Original paper language: Russian
Citation: I. B. Penkov, A. S. Tikhomirov, “Triviality of vector bundles on twisted ind-Grassmannians”, Mat. Sb., 202:1 (2011), 65–104; Sb. Math., 202:1 (2011), 61–99
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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