manuscripta mathematica

, Volume 36, Issue 2, pp 147–162 | Cite as

Classification of Fano 3-folds with B2≥2

  • Shigefumi Mori
  • Shigeru Mukai


This article contains the classification of Fano 3-folds with B2≥2.

There exist exactly 87 types of such 3-folds up to deformations; a Fano 3-fold is isomorphic to a product of Pl and a del Pezzo surface if its second Betti number is not less than 6. In particular, the second Betti number of a Fano 3-fold is not greater than 10.

Firstly we classify Fano 3-folds which are either primitive or have B2=2 by the tools developed in [2]; then we study Fano 3-folds obtained from them by successive curve-blow-ups by using their conic bundle structures or the existence of lines on them.


Number Theory Algebraic Geometry Topological Group Betti Number Pezzo Surface 
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.


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  1. [1]
    Iskovskih, V.A.: Fano 3-folds I, II, Izv. Akad. Nauk SSSR Ser. Mat. 41, 516–562(1977); 42, 469–506(1978)Google Scholar
  2. [2]
    Mori, S.: Threefolds whose canonical bundles are not numerically effective, Proc. Nat. Akad. Sci. USA vol. 77, 3125–3126(1980)Google Scholar
  3. [3]
    Šokurov, V.V.: The existence of lines on Fano 3-folds, Izv. Akad. Nauk SSSR Ser. Mat. 43, 922–964(1979)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Shigefumi Mori
    • 1
    • 2
  • Shigeru Mukai
    • 1
    • 2
  1. 1.Department of MathematicsNagoya UniversityNagoyaJapan
  2. 2.School of MathematicsInstitute for Advanced StudyPrincetonUSA

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