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.

Non-vanishing theorems for non-split rank 2 bundles on P^3: a simple approach

VALENZANO, Mario
2009-01-01

Abstract

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.
2009
87
1
18
rank two vector bundles; non-vanishing of 1-cohomology
P. Valabrega; M. Valenzano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/75636
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