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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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