Skip to main content
SpringerLink
Log in

On minimal models of elliptic threefolds

  • 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.

References

  1. Brieskorn, E.: Rationale singuläre komplexe Flächen. Invent. Math.4, 336–358 (1968)

    Google Scholar 

  2. Fujita, T.: Fractionally logarithmic canonical rings of algebraic surfaces. J. Fac. Sci. Tokyo Univ.IA 30, 685–696 (1984)

    Google Scholar 

  3. Fujita, T.: Zariski decomposition and canonical rings of elliptic 3-folds. J. Math. Soc. Japan38, 20–37 (1986)

    Google Scholar 

  4. Grassi, A., Minimal models of elliptic threefolds. Ph.D. Thesis, Duke University (1990)

  5. Grassi, A.: Some applications of Mori theory to elliptic threefolds. (In preparation)

  6. Grassi, A.: The singularities of the parameter surface of a minimal elliptic threefold. (Preprint)

  7. Hironaka, H.: Flattening theorem in complex-analytic geometry. Am. J. Math.97, 503–547 (1975)

    Google Scholar 

  8. Kawamata, Y.: Kodaira dimension of certain algebraic fiber spaces. J. Fac Sci. Tokyo Univ. IA30, 1–24 (1983)

    Google Scholar 

  9. Kawamata, Y.: The cone of curves of algebraic varieties. Ann. Math.119, 603–633 (1984)

    Google Scholar 

  10. Kawamata, Y.: Minimal models and the Kodaira dimension of algebraic fiber spaces. J. Reine Angew. Math.363, 1–46 (1985)

    Google Scholar 

  11. Kawamata, Y.: On eh plurigenera of minimal algebraic 3-folds withK≈0, Math. Ann.275, 1–24 (1986)

    Google Scholar 

  12. Kawamata, Y., Matsuda, K., Matsuki, K.: Introduction to the minimal model problem. in: Proc. Sym. Alg. Geom. Sendai 1985, Adv. Stud. Pure Math10, 283–360 (1985)

  13. Kollár, J.: Higher direct images of dualizing sheaves I. Ann. Math.1123, 11–42 (1986)

    Google Scholar 

  14. Kodaira, K.: On compact analytic surfaces, II, III. Ann. Math.77, 78, 563–626, 1–40 (1963)

    Google Scholar 

  15. Mori, S.: Flip theorem and the existence of minimal models for 3-folds. J. Amer. Math. Soc.1, 117–253 (1988)

    Google Scholar 

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

    Google Scholar 

  17. Nakayama, N.: The singularities of the canonical model of complex Kähler manifolds. Math. Ann.280, 509–512 (1988)

    Google Scholar 

  18. Nakayama, N.: On Weierstrass models. Algebraic geometry and commutative algebra, in honor of M. Nagata, pp. 405–431, Tokyo: Kinokunyia 1987

    Google Scholar 

  19. Sakai, F.: Anti-Kodaira dimension of ruled surfaces. Sci. Rep. Saitama University Ser. A10, 1–7 (1982)

    Google Scholar 

  20. Sakai, F.: Classification of normal surfaces, in: Algebraic geometry Bowdoin. Proc. Symp. Pure Math.46, 451–465 (1987)

    Google Scholar 

  21. Wilson, P.M.H.: Towards birational classification of algebraic varieties. Bull. Lond. Math. Soc.19, 1–48 (1987)

    Google Scholar 

  22. Zariski, O.: The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface. Ann. Math.76, 560–615 (1962)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Tufts University, 02155, Medford, MA, USA

    Antonella Grassi

Authors
  1. Antonella Grassi
    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

Grassi, A. On minimal models of elliptic threefolds. Math. Ann. 290, 287–301 (1991). https://doi.org/10.1007/BF01459246

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01459246

Keywords

Search

Navigation