Advertisement

manuscripta mathematica

, Volume 64, Issue 2, pp 189–204 | Cite as

On Fano 3-folds

  • Steven Dale Cutkosky
Article

Abstract

In this paper Fano 3-folds of the principal series and first species are classified.

Keywords

Number Theory Algebraic Geometry Topological Group Principal Series 
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. [E]
    R. Elkik, Rationalite des singularities canonique, Invent. Math., 64 (1981), 1–6Google Scholar
  2. [I1]
    V.A. Iskovskih, Fano 3-folds I, Math. USSR-Izv., 11 (1977), 485–527Google Scholar
  3. [I2]
    —, Fano 3-folds II, Math. USSR-Izv., 12 (1978), 469–506Google Scholar
  4. [M1]
    S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math., (2) 116 (1982), 133–176Google Scholar
  5. [M2]
    -, Lectures on Fano threefolds, Columbia University, Fall 1986Google Scholar
  6. [M-M]
    S. Mori and S. Mukai, Classification of Fano 3-folds with B2≥2, Manuscripta Math. 36, (1981), 149–162Google Scholar
  7. [M-U]
    S. Mukai and H. Umemura, Minimal rational threefolds, Algebraic Geometry, Proceedings, Tokyo/Kyoto 1982, Lecture Notes in Math. 1016, Springer-Verlag, Heidelberg (1983), 490–518Google Scholar
  8. [Mu]
    J.P. Murre, Classification of Fano threefolds according to Fano and Iskovskih, Algebraic Threefolds, Lecture Notes in Math. 947, Springer-Verlag, Heidelberg (1982), 35–92Google Scholar
  9. [R1]
    M. Reid, Canonical 3-folds, in Journees de Geometrie algebrique d'Angers, ed. A. Beauville, Sijthoff and Noordhoff, Alphen, (1980), 273–310Google Scholar
  10. [R2]
    —, Minimal models of canonical 3-folds, in Advanced Studies in Pure Mathematics 1, Algebraic and Analytic Varieties, Kinokuniya, Tokyo (1983),131–180Google Scholar
  11. [SB]
    N. Shepherd-Barron, Some questions on singularities in 2 and 3 dimensions, Warwick Thesis, 1980Google Scholar
  12. [SD]
    B. Saint-Donat, Projective models of K3 surfaces, Amer. J. Math. 96 (1974), 602–639Google Scholar
  13. [S]
    V.V. Sokurov, The existence of lines on Fano threefolds, Math. USSR-Izv., 15 (1980), 173–209Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Steven Dale Cutkosky
    • 1
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

Personalised recommendations