Skip to main content
Log in

The moduli space of 3-folds withK=0 may nevertheless be irreducible

  • 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

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

Instant access to the full article PDF.

References

  1. Artin, M.: Algebraization of formal moduli. II. Existence of modifications. Ann. Math.91, 88–135 (1970)

    Google Scholar 

  2. Atiyah, M.F.: On analytic surfaces with double points. Proc. Royal Soc. A247, 237–244 (1958)

    Google Scholar 

  3. Brieskorn, E.: Über die Auflösungen gewisser Singularitäten von holomorphen Abbildungen. Math. Ann.166, 76–102 (1966)

    Google Scholar 

  4. Brieskorn, E.: Die Auflösungen der rationalen Singularitäten von holomorphen Abbildungen. Math. Ann.178, 255–270 (1968)

    Google Scholar 

  5. Burns, D., Rapoport, M.: The Torelli problem for Kählerian K3 surfaces. Ann. Sci. Ecole Norm. Super8, 235–273 (1975)

    Google Scholar 

  6. Clemens, H.: Double solids. Adv. Math.47, 107–230 (1983)

    Google Scholar 

  7. Clemens, H.: Homological equivalence modulo algebraic equivalence is not finitely generated. Publ. Math. IHES58, 19–38 (1983)

    Google Scholar 

  8. Enriques, F.: Le superficie algebriche. Bologna: Zanichelli, 1946

    Google Scholar 

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

    Google Scholar 

  10. Grauert, H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann.146, 331–368 (1962)

    Google Scholar 

  11. Griffiths, P.A.: On the periods of certain rational integrals II. Ann. Math.90, 496–541 (1969)

    Google Scholar 

  12. Griffiths, P.A., Harris, J.: On the Noether-Lefschetz theorem and some remarks on codimension 2 cycles. Math. Ann.271, 31–51 (1985)

    Google Scholar 

  13. Hirzebruch, F.: Some examples of threefolds with trivial canonical bundle, notes by J. Werner. Max Planck Inst. preprint no. 85-58, Bonn 1985

  14. Kodaira, K.: On the structure of compact complex analytic surfaces I. Am. J. Math.86, 751–798 (1964), collected works p. 1389

    Google Scholar 

  15. Mayer, A.: Families of K 3 surfaces. Nagoya Math. J.48, 1–17 (1972)

    Google Scholar 

  16. Mori, S.: Flip conjecture and existence of minimal models for 3-folds (in preparation)

  17. Reid, M.: Minimal models of canonical 3-folds. In: Advanced studies in Pure Math.1. Algebraic varieties and analytic varieties, 131–180, S. Iitaka and H. Morikawa (eds.). Amsterdam, New York, Oxford: Kinokuniya and North-Holland, 1983

    Google Scholar 

  18. Todorov, A.: Application of Calabi-Yau metric to the Weil-Petersson metric and to the Teichmüller space of complex manifold withK=0. Max Planck Inst. preprint no. 86-41, Bonn 1986

  19. Tyurina, G.N.: The moduli space of complex surfaces withq=0 andK=0. In: I.R. Shafarevich, Algebraic surfaces, Proc. Steklov Inst.75, Chap. IX (1965)

  20. Wall, C.T.C.: Classification problems in topology V: on certain 6-manifolds. Invent. Math.1, 355–374 (1966)

    Google Scholar 

  21. Werner, J.: Kleine Auflösungen spezieller dreidimensionaler Varietäten. Thesis (in preparation) (Bonn)

Download references

Author information

Authors and Affiliations

Authors

Additional information

To Friedrich Hirzebruch on his sixtieth birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reid, M. The moduli space of 3-folds withK=0 may nevertheless be irreducible. Math. Ann. 278, 329–334 (1987). https://doi.org/10.1007/BF01458074

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01458074

Keywords

Navigation