Advertisement

Inventiones mathematicae

, Volume 122, Issue 1, pp 403–419 | Cite as

Global smoothing of Calabi-Yau threefolds

  • Yoshinori Namikawa
  • J. H. M. Steenbrink
Article

Keywords

Global Smoothing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AC] A'Campo, N.: Le nombre de Lefschetz d'une monodromie. Indag. Math. (N.S.)8, 113–118 (1973)Google Scholar
  2. [Be] Beauville, A.: Variétés Kähleriennes dont la première classe de Chern est nulle. J. Differ. Geom.18, 755–782 (1983)Google Scholar
  3. [C1] Clemens, H.: Double solids, Adv. Math.47, 107–230 (1983)Google Scholar
  4. [Di] Dimca, A.: Betti numbers of hypersurfaces and defects of linear systems. Duke Math. J.60, 285–298 (1990)Google Scholar
  5. [Fr] Friedman, R.: Simultaneous resolution of threefold double points. Math. Ann.274, 671–689 (1986)Google Scholar
  6. [G-H] Green, P.S., Hübsh, T.: Connecting moduli spaces of Calabi-yau threefolds. Comm. Math. Phys.119, 431–441 (1988)Google Scholar
  7. [H] Hirzebruch, F.: Some examples of threefolds with trivial canonical bundle. M.P.I. preprint, no. 85-58, Bonn (1985)Google Scholar
  8. [Ka 1] Kawamata, Y.: Crepant blowing-up of 3-dimensional canonical singularities and its application of degenerations of surfaces. Ann. Math.127(2), 93–163 (1988)Google Scholar
  9. [Ka 2] Kawamata, Y.: Minimal models and the Kodaira dimension of algebraic fiber spaces. J. Reine Angew. Math.363, 1–46 (1986)Google Scholar
  10. [Ka 3] Kawamata, Y.: Abundance theorem for minimal threefolds. preprint (1991)Google Scholar
  11. [Ka 4] Kawamata, Y.: Unobstructed deformations, a remark on a paper of Z. Ran. J. Algebraic Geom.1, 183–190 (1992)Google Scholar
  12. [K-M-M] Kawamata, Y., Matsuda, K., Matsuki, K.: Introduction to the minimal model problem. Adv. Stu. Pure Math.10, 283–360 (1987), Kinokuniya and North-HollandGoogle Scholar
  13. [K-M] Kollár, J., Mori, S.: Classification of three-dimensional flips. J. Am. Math. Soc.5(3), 533–703Google Scholar
  14. [Ko] Kollár, J.: Shafarevich maps and plurigenera of algebraic varieties. Invent. Math.113, 177–215 (1993)Google Scholar
  15. [Lo] Looijenga, E.J.N.: Isolated singular points on complete intersections. London Math. Soc. Lect. Note. Ser.77, Cambridge University Press 1984Google Scholar
  16. [Mo] Mori, S.: Flip theorem and the existence of minimal threefolds. J. Am. Math. Soc.1, 117–253 (1988)Google Scholar
  17. [Na] Namikawa, Y.: On deformations of Calabi-Yau threefolds with terminal singularities. Topology33(3), 429–446 (1994)Google Scholar
  18. [Ra] Ran, Z.: Deformations of Calabi-Yau Kleinfolds. In: Essays on Mirror manifoldsGoogle Scholar
  19. [Re 1] Reid, M.: Minimal models of canonical threefolds. Adv. Stud. Pure Math.1, 131–180 (1983) Kinokuniya, North-HollandGoogle Scholar
  20. [Re 2] Reid, M.: The moduli space of threefolds withK=0 may nevertheless be irreducible. Math. Ann.278, 329–334 (1987)Google Scholar
  21. [S-S] Scherk, J., Steenbrink, J.H.M.: On the mixed Hodge structure on the cohomology of the Milnor fibre. Math. Ann.271, 641–665 (1985)Google Scholar
  22. [Sch] Schlessinger, M.: Rigidity of quotient singularities. Invent. Math.14, 17–26 (1971)Google Scholar
  23. [St 1] Steenbrink, J.H.M.: Mixed Hodge structure on the vanishing cohomology, In: Real and complex singularities, Oslo 1976. P. Holm ed. pp. 525–563, Sijthoff-Noordhoff, Alphen a/d Rijn 1977Google Scholar
  24. [St 2] Steenbrink, J.H.M.: Mixed Hodge structures associated with isolated singularities. Proc. Symp. Pure Math.40 Part 2, 513–536 (1983)Google Scholar
  25. [St 3] Steenbrink, J.H.M.: Vanishing theorems on singular spaces. Astérisque130, 330–341 (1985)Google Scholar
  26. [Te] Teissier, B.: The hunting of invariants in the geometry of discriminants. In: Real and complex singularities, Oslo 1976. P. Holm ed. pp. 565–677, Sijthoff-Noordhoff, Alphen a/d Rijn 1977Google Scholar
  27. [W] Werner, J.: Kleine Auflösungen spezieller dreidimensionaler Varietäten. Bonner Math. Schriften Nr.186 (1987)Google Scholar
  28. [Wi] Wilson, P.M.H.: Calabi-Yau manifolds with large Picard number. Invent. Math.98, 139–155 (1989)Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Yoshinori Namikawa
    • 1
  • J. H. M. Steenbrink
    • 2
  1. 1.Department of MathematicsSophia UniversityTokyo 102Japan
  2. 2.Mathematical InstituteUniversity of NijmegenNijmegenThe Netherlands

Personalised recommendations