Izvestiya: Mathematics
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


Izvestiya: Mathematics, 2006, Volume 70, Issue 5, Pages 867–882
DOI: https://doi.org/10.1070/IM2006v070n05ABEH002331
(Mi im616)
 

This article is cited in 2 scientific papers (total in 2 papers)

Holomorphic bundles on diagonal Hopf manifolds

M. S. Verbitsky

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
References:
Abstract: We show that every stable holomorphic bundle on the Hopf manifold $M=(\mathbb C^n\setminus0)/\langle A\rangle$ with $\dim M\geqslant 3$, where $A\in\operatorname{GL}(n,\mathbb C)$ is a diagonal linear operator with all eigenvalues satisfying $|\alpha_i|<1$, can be lifted to a $\widetilde G_F$-equivariant coherent sheaf on $\mathbb C^n$, where $\widetilde G_F\cong(\mathbb C^*)^l$ is a commutative Lie group acting on $\mathbb C^n$ and containing $A$. This is used to show that all bundles on $M$ are filtrable, that is, admit a filtration by a sequence $F_i$ of coherent sheaves with all subquotients $F_i/F_{i-1}$ of rank $1$.
Received: 30.08.2005
Revised: 16.06.2006
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2006, Volume 70, Issue 5, Pages 13–30
DOI: https://doi.org/10.4213/im616
Bibliographic databases:
UDC: 515.171.3+515.174.5
MSC: 53C55, 14J60
Language: English
Original paper language: Russian
Citation: M. S. Verbitsky, “Holomorphic bundles on diagonal Hopf manifolds”, Izv. RAN. Ser. Mat., 70:5 (2006), 13–30; Izv. Math., 70:5 (2006), 867–882
Citation in format AMSBIB
\Bibitem{Ver06}
\by M.~S.~Verbitsky
\paper Holomorphic bundles on diagonal Hopf manifolds
\jour Izv. RAN. Ser. Mat.
\yr 2006
\vol 70
\issue 5
\pages 13--30
\mathnet{http://mi.mathnet.ru/im616}
\crossref{https://doi.org/10.4213/im616}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2269707}
\zmath{https://zbmath.org/?q=an:1147.53058}
\elib{https://elibrary.ru/item.asp?id=9296567}
\transl
\jour Izv. Math.
\yr 2006
\vol 70
\issue 5
\pages 867--882
\crossref{https://doi.org/10.1070/IM2006v070n05ABEH002331}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000243560600002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846635527}
Linking options:
  • https://www.mathnet.ru/eng/im616
  • https://doi.org/10.1070/IM2006v070n05ABEH002331
  • https://www.mathnet.ru/eng/im/v70/i5/p13
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:890
    Russian version PDF:362
    English version PDF:17
    References:58
    First page:3
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024