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Fano 4-folds of index 2 with $$b_ 2\geqslant 2$$. A contribution to Mukai classification. (English) Zbl 0766.14036
The author presents a proof of the classification of all Fano 4-folds of index 2 with second Betti number $$\geq 2$$, under the assumption that there is a smooth divisor $$H$$ such that $$-2H$$ is a canonical divisor of $$X$$. The classification of all Fano manifolds of coindex 3 was announced by S. Mukai in 1982 [see S. Mukai, Fano manifolds of coindex 3: Preprint (Univ. Warwick 1982); see also Proc. Natl. Acad. Sci. USA 86, No. 9, 3000-3002 (1989; Zbl 0679.14020)].

##### MSC:
 14J45 Fano varieties 14J35 $$4$$-folds 14J10 Families, moduli, classification: algebraic theory
##### Keywords:
classification; Fano 4-folds; index; second Betti number