Skip to main content
SpringerLink
Log in

Ladders on Fano varieties

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We prove the existence of ladders on log Fano varieties of coindex less than 4, as an application of adjunction and nonvanishing.

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. V. Alexeev, “Theorem about good divisors on log Fano varieties,”Lect. Notes Math.,1479, 1–9 (1991).

    MATH  MathSciNet  Google Scholar 

  2. T. Fujita, “Classification theories of polarized varieties,” In:London Math. Soc. Lect. Note Series, Vol. 155 (1990).

  3. R. Hartshorne,Algebraic Geometry, Springer-Verlag, New York-Heidelberg (1977).

    Google Scholar 

  4. S. Helmke, “On Fujita’s conjecture,”Duke Math. J.,88:2, 201–216 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  5. Y. Kawamata,On Fujita’s freeness conjecture for 3-folds and 4-folds, preprint (1996).

  6. Y. Kawamata,Subadjunction of log canonical divisors for a subvariety of codimension 2, preprint (1996).

  7. Y. Kawamata,Subadjunction of log canonical divisors, II, preprint (1997).

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

    MathSciNet  Google Scholar 

  9. M. Mella,Existence of good divisors on Mukai manifolds, preprint (1996).

  10. M. Mella,Existence of good divisors on Mukai varieties, preprint (1997).

  11. Yu. G. Prokhorov, “On algebraic threefolds whose hyperplane sections are Enriques surfaces,”Mat. Sb.,186, No. 9, 1341–1352 (1995).

    MATH  MathSciNet  Google Scholar 

  12. M. Reid,Projective morphisms according to Kawamata, preprint, Univ. of Warwick (1983).

  13. T. Sano, “Classification ofℚ-Fanod-folds of index greater thand — 2,”Nagoya Math. J.,142, 133–143 (1996).

    MATH  MathSciNet  Google Scholar 

  14. K.-H. Shin, “3-Dimensional Fano varieties with canonical singularities,”Tokyo J. Math.,12, 375–385 (1989).

    MATH  MathSciNet  Google Scholar 

  15. V. V. Shokurov, “Smoothness of the general anticanonical divisor of a Fano 3-fold,”Izv. Akad. Nauk SSSR, Ser. Mat.,14, 395–405 (1980).

    MATH  Google Scholar 

  16. V. V. Shokurov, “The nonvanishing theorem,”Izv. Akad. Nauk SSSR, Ser. Mat.,26, 591–604 (1986).

    MATH  Google Scholar 

  17. V. V. Shokurov, “3-Fold log flips,”Izv. Rossiisk. Akad. Nauk, Ser. Mat.,40, No. 1 (1993).

Download references

Authors
  1. F. Ambro
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 56. Algebraic Geometry-9, 1998.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ambro, F. Ladders on Fano varieties. J Math Sci 94, 1126–1135 (1999). https://doi.org/10.1007/BF02367253

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02367253

Keywords

Search

Navigation