Skip to main content
SpringerLink
Log in

Small contractions of four dimensional algebraic manifolds

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

References

  1. Ando, T.: On extremal rays of the higher dimensional varieties. Invent. Math.81, 347–357 (1985)

    Google Scholar 

  2. Beltrametti, M.: Ond-folds whose canonical bundle is not numerically effective according to Mori and Kawamata. Ann. Mat. Pura Appl.147, 151–172 (1987)

    Google Scholar 

  3. Beltrametti, M.: Contractions of non numerically effective extremal rays in dimension 4, Proc. Alg. Geom. Teubner-Texte Math. 92, 24–37, Berlin: Teubner 1986

    Google Scholar 

  4. Cutkosky, S.: Elementary contractions of Govenstein threefolds, Math. Ann.280, 521–525 (1988)

    Google Scholar 

  5. Friedman, R.: Simultaneous resolution of threefold double points. Math. Ann.274, 671–689 (1986)

    Google Scholar 

  6. Ionescu, P.: Generalized adjunction and applications. Math. Proc. Camb. Phil. Soc.99, 452–472 (1986)

    Google Scholar 

  7. Kawamata, Y.: On the finiteness of generators of a pluri-canonical ring for a 3-fold of general type. Am. J. Math.106, 1503–1512 (1984)

    Google Scholar 

  8. Kawamata, Y.: Crepant blowing-up of 3-dimensional canonical singularities and its application to degeneration of surfaces. Ann. Math.127, 93–163 (1988)

    Google Scholar 

  9. Kawamata, Y., Matsuda, K., Matsuki, K.: Introduction to the minimal model problem. Adv. St. Pure Math.10, 283–360 (1987)

    Google Scholar 

  10. Miyaoka, Y., Mori, S.: A numerical criterion for uniruledness. Ann. Math.124, 65–69 (1986)

    Google Scholar 

  11. Mori, S.: Threefolds whose canonical bundles are not numerically effective. Ann. Math.116, 133–176 (1982)

    Google Scholar 

  12. Okonek, C., Schneider, M., Spindler, H.: Vector bundles on complex projective spaces. Progress in Math. 3. Basel: Birkhäuser 1980

    Google Scholar 

  13. Pinkham, H.: Factorization of birational maps in dimension 3. Proc. Symp. Pure Math.40, 343–371 (1983)

    Google Scholar 

  14. Reid, M.: Minimal models of canonical 3-folds. Adv. St. Pure Math.1, 131–180 (1983)

    Google Scholar 

  15. Van de Ven, A.: On uniform vector bundles. Math. Ann.195, 245–248 (1972)

    Google Scholar 

  16. Wilson, P.M.H.: Fano fourfolds of index greater than one. J. reine angew. Math.379, 172–181 (1987)

    Google Scholar 

  17. Wisniewski, J.: Length of extremal rays and a characterization of projective space, preprint, Notre Dame, 1987

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Tokyo, Hongo, 113, Tokyo, Japan

    Yujiro Kawamata

Authors
  1. Yujiro Kawamata
    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

Kawamata, Y. Small contractions of four dimensional algebraic manifolds. Math. Ann. 284, 595–600 (1989). https://doi.org/10.1007/BF01443353

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01443353

Keywords

Search

Navigation