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

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

2007-10-11

arxiv.org/abs/0710.2242v2

Mathematics

Algebraic Geometry

18 pages, 2 figures, section 2 and 4 revisited, section 3 expanded, new introduction and abstract

Scientific paper

The paper investigates vanishing conditions on the first cohomology module of a normalized rank 2 vector bundle E on P^3 which force E 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.

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