Loading [MathJax]/jax/output/CommonHTML/jax.js
Mathematics of the USSR-Izvestiya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mathematics of the USSR-Izvestiya, 1976, Volume 10, Issue 6, Pages 1187–1204
DOI: https://doi.org/10.1070/IM1976v010n06ABEH001832
(Mi im2259)
 

This article is cited in 22 scientific papers (total in 23 papers)

Vector bundles of finite rank over infinite varieties

A. N. Tyurin
References:
Abstract: This article contains a proof of the conjecture of Schwarzenberger that vector bundles on infinite-dimensional projective space P split as the sum of line bundles, and a generalization to quasi-homogeneous projective varieties.
Bibliography: 7 titles.
Received: 06.10.1975
Bibliographic databases:
UDC: 513.6
MSC: Primary 14F05; Secondary 14M10, 14N05
Language: English
Original paper language: Russian
Citation: A. N. Tyurin, “Vector bundles of finite rank over infinite varieties”, 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 Math. USSR-Izv.
\yr 1976
\vol 10
\issue 6
\pages 1187--1204
\mathnet{http://mi.mathnet.ru/eng/im2259}
\crossref{https://doi.org/10.1070/IM1976v010n06ABEH001832}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=453744}
\zmath{https://zbmath.org/?q=an:0346.14006}
Linking options:
  • https://www.mathnet.ru/eng/im2259
  • https://doi.org/10.1070/IM1976v010n06ABEH001832
  • https://www.mathnet.ru/eng/im/v40/i6/p1248
  • This publication is cited in the following 23 articles:
    1. E Ballico, “Extending Infinitely Many Times Arithmetically Cohen–Macaulay and Gorenstein Subvarieties of Projective Spaces”, The Quarterly Journal of Mathematics, 73:2 (2022), 701  crossref
    2. 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
    3. Cristian Anghel, Springer Proceedings in Mathematics & Statistics, 263, Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1, 2018, 385  crossref
    4. 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
    5. 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
    6. 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
    7. S. M. Ermakova, “O prostranstve putei na polnykh peresecheniyakh v grassmanianakh”, Model. i analiz inform. sistem, 21:4 (2014), 35–46  mathnet
    8. A. L. Onishchik, E. G. Vishnyakova, “Locally free sheaves on complex supermanifolds”, Transformation Groups, 2013  crossref
    9. Iustin Coandă, “A Simple Proof of Tyurin's Babylonian Tower Theorem”, Communications in Algebra, 40:12 (2012), 4668  crossref
    10. 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
    11. Iustin Coandă, “Infinitely stably extendable vector bundles on projective spaces”, Arch Math, 2010  crossref
    12. Ivan Penkov, Alexander S. Tikhomirov, Progress in Mathematics, 270, Algebra, Arithmetic, and Geometry, 2009, 555  crossref
    13. I. Coandă, G. Trautmann, “The Splitting Criterion of Kempf and the Babylonian Tower Theorem”, Communications in Algebra, 34:7 (2006), 2485  crossref
    14. 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
    15. E. Ballico, “Union of linear spaces in infinite-dimensional projective spaces and holomorphic vector bundles”, Results. Math, 43:3-4 (2003), 202  crossref
    16. E. Ballico, “Topologically trivial holomorphic vector bundles on infinite-dimensional projective varieties”, Results. Math, 44:1-2 (2003), 35  crossref
    17. László Lempert, “The Dolbeault complex in infinite dimensions I”, J. Amer. Math. Soc., 11:3 (1998), 485  crossref
    18. H. Flenner, “Babylonian tower theorems for coverings”, Arch. Math, 57:3 (1991), 299  crossref
    19. E. Graham Evans, Phillip Griffith, “Filtering cohomology and lifting vector bundles”, Trans. Amer. Math. Soc., 289:1 (1985), 321  crossref
    20. Hubert Flenner, “Babylonian tower theorems on the punctured spectrum”, Math. Ann., 271:1 (1985), 153  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:478
    Russian version PDF:160
    English version PDF:29
    References:67
    First page:1
     
      Contact us:
    math-net2025_03@mi-ras.ru
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025