THREEFOLDS CONTAINING BORDIGA SURFACES AS AMPLE DIVISORS

Let L be an ample line bundle on a smooth complex projective variety X of dimension three such that there exists a smooth member Z of vertical bar L vertical bar. When the restriction L(Z) of L to Z is very ample and (Z, L(Z)) is a Bordiga surface, it is proved that there exists all ample vector bundle E of rank two on P(2) with c(1) (epsilon) = 4 and 3 <= c(2)(epsilon) <= 10 such that (X, L) = (P(p2)(epsilon), H(epsilon)), where H(epsilon) is the tautological line bundle on the projective space bundle P(p2) (epsilon) associated to epsilon.