Non-vanishing theorems for rank 2 bundles on P^3: a simple approach without the speciality lemma

摘要

The paper investigates vanishing conditions on the first cohomology module ofa normalized rank 2 vector bundle E on P^3 which force E to split, and findstherefore strategic levels of non-vanishing for a non-split bundle. The presentconditions improve other conditions known in the literature and are obtainedwith simple computations on the Euler characteristic function, avoiding thespeciality lemma, Barth's restriction theorem, the discriminat property, andother heavy tools.