Skip to main content
SpringerLink
Log in

Existence of rank 3 vector bundles with given chern classes on homogeneous rational 3-folds

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

One proves that any rank 3 topological vector bundle on a homogeneous rational 3-fold has an algebraic structure. The proof uses extensions of ideals by rank 2 vector bundles. The paper also contains a construction of rank 3 vector bundles on 3-folds using extensions of ideals by rank 2 reflexive sheaves.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. ATIYAH,M.F., REES,E.: Vector bundles on projective 3-space. Invent. Math.,35, 131–153 (1976)

    Google Scholar 

  2. BANICA,C., PUTINAR,M.: On complex vector bundles on rational threefolds. Preprint Increst,64, December (1983)

  3. FERRAND,D.: Courbes gauches et fibrés de rang 2. C. R. Acad. Sci. Paris,281, A, 345–347 (1975)

    Google Scholar 

  4. HARTSHORNE,R.: Stable vector bundles of rank 2 on |P3. Math. Ann.238, 229–280 (1978)

    Google Scholar 

  5. HARTSHORNE,R.: Stable reflexive sheaves. Math. Ann.254, 121–176 (1980)

    Google Scholar 

  6. HORROCKS,G.: A construction for locally free sheaves. Topology7, 117–120 (1968)

    Google Scholar 

  7. KEMPF,G., LAKSOV, D.: The determinantal formula of Schubert calculus. Acta Math.132, 153–162 (1974)

    Google Scholar 

  8. OKONEK,C.,SCHNEIDER,M.,SPINDLER,H.: Vector bundles on complex projective spaces. Boston-Basel-Stuttgart: Birkhăuser 1980

    Google Scholar 

  9. SCHWARZENBERGER,R.L.E.: Vector bundles on algebraic surfaces. Proc. London Math. Soc.11,601–622 (1961)

    Google Scholar 

  10. SERRE,J.P.: Sur les modules projectifs. Sém. Dubreil-Pisot 1960/61 exposé 2

  11. SPINDLER,H.: Die Modulräume stabiler 3-Bündel auf |P3 mit den Chernklassen c1=0, c3=c 22 -c2. Math. Ann.256, 133–143 (1981)

    Google Scholar 

  12. VOGELAAR,J.A.: Constructing vector bundles from co-dimension-two subvarieties. Thesis. Leiden (1978)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, INCREST, Bd. Păcii 220, 79622, Bucharest, Romania

    Constantin Bănică & Justin Coandă

Authors
  1. Constantin Bănică
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Justin Coandă
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bănică, C., Coandă, J. Existence of rank 3 vector bundles with given chern classes on homogeneous rational 3-folds. Manuscripta Math 51, 121–143 (1985). https://doi.org/10.1007/BF01168349

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01168349

Keywords

Search

Navigation