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We consider weak Fano manifolds with small contractions obtained by blowingup successively curves and subvarieties of codimension 2 in products ofprojective spaces. We give a classification result for a special case. In theprocess of proof, we describe explicitly the structure of nef cones and computethe self intersection numbers of anti-canonical divisors for such weak Fanomanifolds.

On weak Fano manifolds with small contractions obtained by blow-ups of a product of projective spaces