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

Svetlana Ermakova

Complex Manifolds (2015)

  • Volume: 2, Issue: 1, page 78-88, electronic only
  • ISSN: 2300-7443

Abstract

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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.

How to cite

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Svetlana Ermakova. "Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians." Complex Manifolds 2.1 (2015): 78-88, electronic only. <http://eudml.org/doc/275958>.

@article{SvetlanaErmakova2015,
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.},
author = {Svetlana Ermakova},
journal = {Complex Manifolds},
keywords = {Vector bundles; Barth-Van de Ven-Tyurin-Sato theorem; ind-varieties; vector bundles; Barth-Van de ven-Tyurin-Sato theorem},
language = {eng},
number = {1},
pages = {78-88, electronic only},
title = {Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians},
url = {http://eudml.org/doc/275958},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Svetlana Ermakova
TI - Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians
JO - Complex Manifolds
PY - 2015
VL - 2
IS - 1
SP - 78
EP - 88, electronic only
AB - 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.
LA - eng
KW - Vector bundles; Barth-Van de Ven-Tyurin-Sato theorem; ind-varieties; vector bundles; Barth-Van de ven-Tyurin-Sato theorem
UR - http://eudml.org/doc/275958
ER -

References

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  1. [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. Zbl0299.14024
  2. [2] Donin J., Penkov I. Finite rank vector bundles on inductive limits of Grassmannians, IMRN. 2003. No 34. P. 1871-1887. Zbl1074.14530
  3. [3] Griffiths P. A., Harris J. Principles of Algebraic Geometry, New York: Wiley, 1978. Zbl0408.14001
  4. [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. Zbl0362.14005
  5. [5] Penkov I., Tikhomirov A.S. Linear ind-Grassmannians, Pure and Applied Mathematics Quarterly. 2014. 10. N-2. P.289-323. [WoS] 
  6. [6] Penkov I., Tikhomirov A.S. On the Barth–Van de Ven–Tyurin–Sato theorem, arXiv:1405.3897 [math.AG]. [WoS] 
  7. [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. Zbl1200.14102
  8. [8] Tyurin A. N. Vector bundles of finite rank over infinite varieties, Math. USSR. Izvestija. 1976. No 10. P. 1187-1204. Zbl0379.14004
  9. [9] Hartshorne R. Algebraic Geometry, New York: Springer-Verlag, 1977. 
  10. [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). 
  11. [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). 
  12. [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). 
  13. [13] Шафаревич И. Р. Основы алгебраической геометрии,МЦНМО, Москва, 2007. (English translation: Shafarevich I.R. Foundations of Algebraic Geometry, MCCME, Moscow. 2007). 

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