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Stable reflexive sheaves. III. (English) Zbl 0607.14009
The author continues his earlier work [cf. part II of this paper, Invent. Math. 66, 165-190 (1982; Zbl 0519.14008)] on stable reflexive sheaves, by determining, for a rank two stable reflexive sheaf on \({\mathbb{P}}^ 3\) with no global sections (not normalized), the best possible upper bound for the third Chern class \(c_ 3\) as a function of \(c_ 1\) and \(c_ 2.\)
As an application, he finds a bound on the genus \(g\) of a nonsingular curve of degree \(d\) in \({\mathbb{P}}^ 3\) which is not contained in any surface of degree \(<k\). This bound is not the best possible, but it gives strong evidence for the conjectural exact bound also stated in this paper.

MSC:
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14H99 Curves in algebraic geometry
57R20 Characteristic classes and numbers in differential topology
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References:
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