NON-VANISHING THEOREMS FOR NON-SPLIT RANK 2 BUNDLES ON P-3 : A SIMPLE APPROACH

The paper investigates vanishing conditions on the first cohomology module of a normalized rank 2 vector bundle epsilon onP(3) which force epsilon to split, and finds therefore strategic levels of non- vanishing for a non- split bundle. The present conditions improve other conditions known in the literature and are obtained with simple computations on the Euler characteristic function, avoiding the speciality lemma, Barth's restriction theorem, the discriminat property, and other heavy tools.