Ruled threefolds homeomorphic to ℙ2 × ℙ1 and their divisors

We study a class of ruled threefolds, namely, manifolds X with a projection p:X→ℙ², such that each fiber is isomorphic to ℙ¹, and which are homeomorphic to ℙ²×ℙ¹; and we characterize ample and very ample line bundles on such threefolds. This paper was written with the financial support of M.P.I. The author is a member of G.N.S.A.G.A. of the C.N.R.