Abstract
Let E be the restriction of the null-correlation bundle on P3 to a hyperplane. In this article, we show that the projective bundle P(E) is isomorphic to a blow-up of a non-singular quadric in P4 along a line. We also prove that for each d≥2, there are hypersurfaces of degree d containing a line in P4 whose blow-up along the line is isomorphic to the projective bundle over P2.
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