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The Chern classes of the stable rank 3 vector bundles on \({\mathbb{P}}^ 3\). (English) Zbl 0588.14010
In an earlier work the author states certain technical conditions which the Chern classes \(c_ 1\), \(c_ 2\) and \(c_ 3\) of a stable rank 3 vector bundle on \({\mathbb{P}}^ 3_ k\) must satisfy after normalizing \(c_ 1\) to \(c_ 1=0, -1\) or -2. In the present work it is shown that if these conditions are satisfied and \(c_ 1c_ 2\equiv c_ 3 mod 2\) for a given set \(c_ 1, c_ 2, c_ 3\) of Chern classes, then there is a stable rank 3 vector bundle on \({\mathbb{P}}^ 3_ k\) with the Chern classes \(c_ 1, c_ 2, c_ 3\). Results of R. Miro on stable rank 2 reflexive sheaves are extended. The author ”adds in proof” that R. Miro has determined the Chern classes of the stable rank 3 reflexive sheaves on \({\mathbb{P}}^ 3\) [R. M. Miro-Roig, Math. Ann. (to appear; see the following review)].
Reviewer: P.Cherenack

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14D20 Algebraic moduli problems, moduli of vector bundles
57R20 Characteristic classes and numbers in differential topology
Full Text: DOI EuDML
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