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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 6, Pages 1248–1268 (Mi izv2259)  

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.

Full text: PDF file (1724 kB)
References: PDF file   HTML file

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
\Bibitem{Tyu76}
\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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Robin Hartshorne, “Stable vector bundles of rank 2 onP 3”, Math Ann, 238:3 (1978), 229  crossref  mathscinet  zmath
    2. 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  crossref  mathscinet  zmath  adsnasa  isi
    3. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. E. Ballico, “Union of linear spaces in infinite-dimensional projective spaces and holomorphic vector bundles”, Results. Math, 43:3-4 (2003), 202  crossref
    5. E. Ballico, “Topologically trivial holomorphic vector bundles on infinite-dimensional projective varieties”, Results. Math, 44:1-2 (2003), 35  crossref
    6. I. Coandă, G. Trautmann, “The Splitting Criterion of Kempf and the Babylonian Tower Theorem”, Communications in Algebra, 34:7 (2006), 2485  crossref
    7. Iustin Coandă, “Infinitely stably extendable vector bundles on projective spaces”, Arch Math, 2010  crossref
    8. I. B. Penkov, A. S. Tikhomirov, “Triviality of vector bundles on twisted ind-Grassmannians”, Sb. Math., 202:1 (2011), 61–99  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Iustin Coandă, “A Simple Proof of Tyurin's Babylonian Tower Theorem”, Communications in Algebra, 40:12 (2012), 4668  crossref
    10. A. L. Onishchik, E. G. Vishnyakova, “Locally free sheaves on complex supermanifolds”, Transformation Groups, 2013  crossref
    11. S. M. Ermakova, “O prostranstve putei na polnykh peresecheniyakh v grassmanianakh”, Model. i analiz inform. sistem, 21:4 (2014), 35–46  mathnet
    12. 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
    13. 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
    14. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    15. 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  mathnet  mathscinet  zmath
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