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We consider weak Fano manifolds with small contractions obtained by blowing up successively curves and subvarieties of codimension 2 in the product of a projective space and a projective line. We give a classification result for a special case. We determine the nef cones and describe the extremal contractions for related smooth projective varieties.

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