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

• Autorzy: Svetlana Ermakova
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 14M10: Complete intersections
• 32L05: Holomorphic bundles and generalizations
• 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2015
• Tom: 2
• Numer: 1

Daty

otrzymano

2015-06-15

zaakceptowano

2015-07-20

online

2015-08-03

Twórcy

autor

Svetlana Ermakova

• P.G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia

Bibliografia

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

Identyfikatory

DOI

10.1515/coma-2015-0007