Fano 4-Folds with scroll structure

Source abstract

Abstract. We classify smooth Fano 4-folds with second betti number b 2 = 2, possesing adjunction theoretic scroll structure. These manifolds occur to be projectivisations of coherent sheaves over Fano manifolds. The paper deals mainly with projectivisations of non-locally free rank 2 Fano sheaves over Fano 3-folds with b 2 = 1, using Mori theory. By the way, we classify nef and big rank 2 bundles over P 2 with the first Chern class (3).