抄録
Let \hat{X} be a smooth connected subvariety of complex projective space Pn. The question was raised in [2] of how to characterize \hat{X} if it admits a reducible hyperplane section \hat{L}. In the case in which \hat{L} is the union of r≥2 smooth normal crossing divisors, each of sectional genus zero, classification theorems were given for dim \hat{X}≥5 or dim \hat{X}=4 and r=2.
This paper restricts attention to the case of two divisors on a threefold, whose sum is ample, and which meet transversely in a smooth curve of genus at least 2. A finiteness theorem and some general results are proven, when the two divisors are in a restricted class including P1-bundles over curves of genus less than two and surfaces with nef and big anticanonical bundle. Next, we give results on the case of a projective threefold \hat{X} with hyperplane section \hat{L} that is the union of two transverse divisors, each of which is either P2, a Hirzebruch surface Fr, or \widetilde{F2}.
