Classification of Fano 3-folds with B2?2

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.