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This article is cited in 14 scientific papers (total in 15 papers)
Vector bundles of finite rank over infinite varieties
A. N. Tyurin
Abstract:
This article contains a proof of the conjecture of Schwarzenberger that vector bundles on infinite-dimensional projective space $P_{\infty}$ split as the sum of line bundles, and a generalization to quasi-homogeneous projective varieties.
Bibliography: 7 titles.
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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:6, 1187–1204
Bibliographic databases:
 
UDC:
513.6
MSC: Primary 14F05; Secondary 14M10, 14N05
Received: 06.10.1975
Citation:
A. N. Tyurin, “Vector bundles of finite rank over infinite varieties”, Izv. Akad. Nauk SSSR Ser. Mat., 40:6 (1976), 1248–1268; Math. USSR-Izv., 10:6 (1976), 1187–1204
Citation in format AMSBIB
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\by A.~N.~Tyurin
\paper Vector bundles of finite rank over infinite varieties
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 6
\pages 1248--1268
\mathnet{http://mi.mathnet.ru/izv2259}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=453744}
\zmath{https://zbmath.org/?q=an:0346.14006}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 6
\pages 1187--1204
\crossref{https://doi.org/10.1070/IM1976v010n06ABEH001832}
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This publication is cited in the following articles:
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Robin Hartshorne, “Stable vector bundles of rank 2 onP 3”, Math Ann, 238:3 (1978), 229
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M. A. Knus, Raman Parimala, R. Sridharan, “Non-free projective modules over ℍ[X, Y] and stable bundles over ℙ2(ℂ)”, Invent math, 65:1 (1981), 13
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F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605
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E. Ballico, “Union of linear spaces in infinite-dimensional projective spaces and holomorphic vector bundles”, Results. Math, 43:3-4 (2003), 202
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E. Ballico, “Topologically trivial holomorphic vector bundles on infinite-dimensional projective varieties”, Results. Math, 44:1-2 (2003), 35
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I. Coandă, G. Trautmann, “The Splitting Criterion of Kempf and the Babylonian Tower Theorem”, Communications in Algebra, 34:7 (2006), 2485
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Iustin Coandă, “Infinitely stably extendable vector bundles on projective spaces”, Arch Math, 2010
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I. B. Penkov, A. S. Tikhomirov, “Triviality of vector bundles on twisted ind-Grassmannians”, Sb. Math., 202:1 (2011), 61–99
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Iustin Coandă, “A Simple Proof of Tyurin's Babylonian Tower Theorem”, Communications in Algebra, 40:12 (2012), 4668
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A. L. Onishchik, E. G. Vishnyakova, “Locally free sheaves on complex supermanifolds”, Transformation Groups, 2013
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S. M. Ermakova, “O prostranstve putei na polnykh peresecheniyakh v grassmanianakh”, Model. i analiz inform. sistem, 21:4 (2014), 35–46
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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
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I. B. Penkov, A. S. Tikhomirov, “On the Barth-Van de Ven-Tyurin-Sato theorem”, Sb. Math., 206:6 (2015), 814–848
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S. M. Ermakova, “Finite-Rank Vector Bundles on Complete Intersections of Finite Codimension in the Linear Ind-Grassmannian”, Math. Notes, 98:5 (2015), 852–856
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M. V. Ignatev, I. Penkov, “Ind-mnogoobraziya obobschennykh flagov: obzor rezultatov”, Trudy seminara po algebre i geometrii Samarskogo universiteta, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 147, VINITI RAN, M., 2018, 3–50
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