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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

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