manuscripta mathematica

, Volume 36, Issue 2, pp 147–162

Classification of Fano 3-folds with B2≥2

  • Shigefumi Mori
  • Shigeru Mukai
Article

DOI: 10.1007/BF01170131

Cite this article as:
Mori, S. & Mukai, S. Manuscripta Math (1981) 36: 147. doi:10.1007/BF01170131

Abstract

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.

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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