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.
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References
Iskovskih, V.A.: Fano 3-folds I, II, Izv. Akad. Nauk SSSR Ser. Mat. 41, 516–562(1977); 42, 469–506(1978)
Mori, S.: Threefolds whose canonical bundles are not numerically effective, Proc. Nat. Akad. Sci. USA vol. 77, 3125–3126(1980)
Šokurov, V.V.: The existence of lines on Fano 3-folds, Izv. Akad. Nauk SSSR Ser. Mat. 43, 922–964(1979)
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Partially supported by Educational Projects for Japanese Mathematical Scientists and NSF Grants MCS 77-15524 and MCS 77-18723 (A04)
Partially supported by Educational Projects for Japanese Mathematical Scientists
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Mori, S., Mukai, S. Classification of Fano 3-folds with B2≥2. Manuscripta Math 36, 147–162 (1981). https://doi.org/10.1007/BF01170131
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DOI: https://doi.org/10.1007/BF01170131