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On the cohomology of certain fibre bundles of rank two on \(\mathbb{P}^ 3\). (Sur la cohomologie de certains fibrés de rang deux sur \(\mathbb{P}^ 3\).) (French) Zbl 0812.14008

The aim of this paper is to show the power of the spectrum for the study of rank 2 vector bundles on \(\mathbb{P}^ 3\) and of their cohomological properties. Using this tool here the author gives all the possible cohomology groups of a rank 2 vector bundle \(E\) on \(\mathbb{P}^ 3\) with \(-1 \leq c_ 1 (E) \leq 0\), \(c_ 2 (E) \leq 4\), \(H^ 0 (\mathbb{P}^ 3, E(-1)) = 0\), \(H^ 0 (\mathbb{P}^ 3,E)) \neq 0\). Furthermore, he gives another proof of a criterion of Chiantini and Valabrega for proving that a subcanonical curve in \(\mathbb{P}^ 3\) is a complete intersection.
Reviewer: E.Ballico (Povo)

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14H50 Plane and space curves
14F20 Étale and other Grothendieck topologies and (co)homologies
14N05 Projective techniques in algebraic geometry
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