Projective Bundles and Blowing-Ups II.

We study the blowing-up X ~ of a smooth projective variety X along a smooth center B that is equipped with a projective bundle structure over a variety Z. If the Picard number ρ (X) is 1 and dim ⁡ X is at most 4, we classify all such pairs (X , B). If X is a projective space P n (n ≥ 5) and dim ⁡ B is 2, we show that B is a linear subspace in X. [ABSTRACT FROM AUTHOR]