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Sbornik: Mathematics, 2015, Volume 206, Issue 6, Pages 814–848
DOI: https://doi.org/10.1070/SM2015v206n06ABEH004480 (Mi sm8384) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On the Barth-Van de Ven-Tyurin-Sato theorem

I. B. Penkova, A. S. Tikhomirovb

a University of Bremen
b Department of Mathematics, National Research University "Higher School of Economics"
English version PDF (724 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2015v206n06ABEH004480
Abstract: The Barth-Van de Ven-Tyurin-Sato Theorem states that any finite-rank vector bundle on the complex projective ind-space $\mathbf{P}^\infty$ is isomorphic to a direct sum of line bundles. We establish sufficient conditions on a locally complete linear ind-variety $\mathbf{X}$ which ensure that the same result holds on $\mathbf{X}$. We then exhibit natural classes of locally complete linear ind-varieties which satisfy these sufficient conditions.
Bibliography: 18 titles.
Keywords: ind-variety, vector bundle.
Funding agency Grant number
Deutsche Forschungsgemeinschaft SPP 1388
We acknowledge the support and hospitality of the Max Planck Institute for Mathematics in Bonn where the present paper was conceived. We also acknowledge partial support from the DFG through Priority Program "Representation Theory" (SPP 1388) at Jacobs University Bremen.
Received: 08.05.2014 and 04.02.2015
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 6, Pages 49–84
DOI: https://doi.org/10.4213/sm8384
Bibliographic databases:
Document Type: Article
UDC: 512.723
MSC: Primary 14M15; Secondary 14J60, 32L05
Language: English
Original paper language: Russian
Citation: I. B. Penkov, A. S. Tikhomirov, “On the Barth-Van de Ven-Tyurin-Sato theorem”, Mat. Sb., 206:6 (2015), 49–84; Sb. Math., 206:6 (2015), 814–848
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
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    References:93
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