Skip to main content
SpringerLink
Log in

On extremal contractions from threefolds to surfaces: The case of one non-Gorenstein point and a nonsingular base surface

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

Abstract

In this paper, we study the local structure of extremal contractionsf∶X→S from threefoldsX with only terminal singularities onto a surfaceS. If the surfaceS is nonsingular andX has a unique non-Gorenstein point on a fiber, we prove that either the linear system ¦−K X ¦, ¦−2K X ¦, or ¦−3K X ¦contains a “good” divisor.

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. A. Beauville, “Variétés de Prym et jacobienne intermédiaires,”Ann. Sci. Ecole Norm. Sup. (4),10, 309–391 (1977).

    Google Scholar 

  2. V. A. Iskovskikh, “On the rationality problem for conic bundles,”Mat. Sb.,182, No. 1, 114–121 (1991).

    Google Scholar 

  3. V. A. Iskovskikh, “On the rationality criterion for conic bundles,”Mat. Sb.,187, No. 7, 75–92 (1996).

    Google Scholar 

  4. Y. Kawamata, “Crepant blowing-ups of 3-dimensional canonical singularities and its application to degenerations of surfaces,”Ann. Math.,127, 93–163 (1988).

    Google Scholar 

  5. S. Mori, “On 3-dimensional terminal singularities,”Nagoya Math. J.,98, 43–66 (1985).

    Google Scholar 

  6. S. Mori, “Flip theorem and the existence of minimal models for 3-folds,”J. Amer. Math. Soc.,1, No. 1, 117–253 (1988).

    Google Scholar 

  7. Yu. G. Prokhorov,On the general elephant conjecture for Mori conic bundles, preprint alg-geom 9608007.

  8. Yu. G. Prokhorov,On extremal contractions from 3-folds to surfaces: the case of one non-Gorenstein point, preprint alg-geom 9605002 (to appear inContemp. Math. AMS).

  9. V. S. Sarkisov, “On conic bundle structures,”Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 2, 371–408 (1982).

    Google Scholar 

  10. V. V. Shokurov, “3-Fold log flips,”Izv. Akad. Nauk SSSR, Ser. Mat.,56, No. 1, 105–201 (1992);57, No. 6, 141–175 (1993).

    Google Scholar 

Download references

Authors
  1. Yu. G. Prokhorov
    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. 45, Algebraic Geometry-8, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Prokhorov, Y.G. On extremal contractions from threefolds to surfaces: The case of one non-Gorenstein point and a nonsingular base surface. J Math Sci 95, 1986–1995 (1999). https://doi.org/10.1007/BF02169156

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02169156

Keywords

Search

Navigation