Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Complex Manifolds

Ed. by Fino, Anna Maria

1 Issue per year


CiteScore 2017: 0.39

SCImago Journal Rank (SJR) 2017: 0.260
Source Normalized Impact per Paper (SNIP) 2017: 0.660

Mathematical Citation Quotient (MCQ) 2016: 0.67


Emerging Science

Open Access
Online
ISSN
2300-7443
See all formats and pricing
More options …

Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians

Svetlana Ermakova
  • Corresponding author
  • P.G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-08-03 | DOI: https://doi.org/10.1515/coma-2015-0007

Abstract

In this article we establish an analogue of the Barth-Van de Ven-Tyurin-Sato theorem.We prove that a finite rank vector bundle on a complete intersection of finite codimension in a linear ind-Grassmannian is isomorphic to a direct sum of line bundles.

Keywords: Vector bundles; Barth-Van de Ven-Tyurin-Sato theorem; ind-varieties

MSC: Primary 14M10; Secondary 14J60; 32L05

References

  • [1] Barth W., Van de Ven A. On the geometry in codimension 2 in Grassmann manifolds, Lecture Notes in Math. 412. Springer- Verlag, 1974. P. 1-35. Google Scholar

  • [2] Donin J., Penkov I. Finite rank vector bundles on inductive limits of Grassmannians, IMRN. 2003. No 34. P. 1871-1887. Google Scholar

  • [3] Griffiths P. A., Harris J. Principles of Algebraic Geometry, New York: Wiley, 1978. Google Scholar

  • [4] Sato E. On the decomposability of infinitely extendable vector bundles on projective spaces and Grassmann varieties, J. Math. Kyoto Univ. 1977. No 17. P. 127-150. Google Scholar

  • [5] Penkov I., Tikhomirov A.S. Linear ind-Grassmannians, Pure and Applied Mathematics Quarterly. 2014. 10. N-2. P.289-323. Web of ScienceGoogle Scholar

  • [6] Penkov I., Tikhomirov A.S. On the Barth–Van de Ven–Tyurin–Sato theorem, arXiv:1405.3897 [math.AG]. Web of ScienceGoogle Scholar

  • [7] Penkov I., Tikhomirov A. S. Rank-2 vector bundles on ind-Grassmannians, Algebra, arithmetic,and geometry: in honor of Yu. I. Manin, V II, Progr. Math., V. 270. Birkhaeuser, Boston-Basel-Berlin, 2009. P. 555-572. Google Scholar

  • [8] Tyurin A. N. Vector bundles of finite rank over infinite varieties, Math. USSR. Izvestija. 1976. No 10. P. 1187-1204. Google Scholar

  • [9] Hartshorne R. Algebraic Geometry, New York: Springer-Verlag, 1977. Google Scholar

  • [10] Ермакова С.М. О пространстве путей на полных пересечениях в грассманианах, МАИС. 2014. Т. 21. No 4. C.35-46 (English translation: Yermakova S.M. On the variety of paths on complete intersections in Grassmannians, MAIS. 2014. V. 21. No 4. P. 35-46). Google Scholar

  • [11] Ермакова С.М. Равномерность векторных расслоений конечного ранга на полных пересечениях конечной коразмерности в линейных инд-грассманианах, МАИС. 2015. Т. 22. No 2. C. 209-2018 (English translation: Yermakova S.M. Uniformity of vector bundles of finite rank on complete intersections of finite codimension in a linear ind- Grassmannian, MAIS. 2015. V. 22. No 2. P. 209-2018). Google Scholar

  • [12] Пенков И.Б., Тихомиров А.С. Тривиальность векторных расслоений на скрученных инд-грассманианах, Математический сборник. 2011. 202. No 1. C. 65-104 (English translation: Penkov I.B., Tikhomirov A.S. Triviality of vector bundles on twisted ind-Grassmannians, Sbornik: Mathematics. 2011. 202, No 1. P. 61-99). Google Scholar

  • [13] Шафаревич И. Р. Основы алгебраической геометрии,МЦНМО, Москва, 2007. (English translation: Shafarevich I.R. Foundations of Algebraic Geometry, MCCME, Moscow. 2007). Google Scholar

About the article

Received: 2015-06-15

Accepted: 2015-07-20

Published Online: 2015-08-03


Citation Information: Complex Manifolds, Volume 2, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2015-0007.

Export Citation

© 2015 Svetlana Ermakova. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in