On weak Fano manifolds with small contractions obtained by blow-ups of a   product of projective spaces
  We consider weak Fano manifolds with small contractions obtained by blowing up successively curves and subvarieties of codimension 2 in products of projective spaces. We give a classification result for a special case. In the process of proof, we describe explicitly the structure of nef cones and compute the self intersection numbers of anti-canonical divisors for such weak Fano manifolds. 
Toru Tsukioka
math.AG