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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) Russian version article
References:
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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
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”, Sb. Math., 202:1 (2011), 61–99
Citation in format AMSBIB
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\by I.~B.~Penkov, A.~S.~Tikhomirov
\paper Triviality of vector bundles on twisted ind-Grassmannians
\jour Sb. Math.
\yr 2011
\vol 202
\issue 1
\pages 61--99
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Linking options:
  • https://www.mathnet.ru/eng/sm7599
  • https://doi.org/10.1070/SM2011v202n01ABEH004138
  • https://www.mathnet.ru/eng/sm/v202/i1/p65
    • This publication is cited in the following 5 articles:
    1. M. V. Ignatyev, I. Penkov, “Ind-Varieties of Generalized Flags: A Survey of Results”, Journal of Mathematical Sciences, 248:3 (2020), 255–302  mathnet  crossref  mathscinet  zmath
    2. S. M. Ermakova, “Ravnomernost vektornykh rassloenii konechnogo ranga na polnykh peresecheniyakh konechnoi korazmernosti v lineinykh ind-grassmanianakh”, Model. i analiz inform. sistem, 22:2 (2015), 209–218  mathnet  mathscinet  elib
    3. I. B. Penkov, A. S. Tikhomirov, “On the Barth-Van de Ven-Tyurin-Sato theorem”, Sb. Math., 206:6 (2015), 814–848  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. S. M. Ermakova, “O prostranstve putei na polnykh peresecheniyakh v grassmanianakh”, Model. i analiz inform. sistem, 21:4 (2014), 35–46  mathnet
    5. I. Penkov, A. S. Tikhomirov, “Linear ind-Grassmannians”, Pure Appl. Math. Q., 10:2 (2014), 289–323  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:593
    Russian version PDF:215
    English version PDF:20
    References:64
    First page:14
     
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