Stable reflexive sheaves. III
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.
bound on genus of curves in projective 3-space
scientific article; zbMATH DE number 3981328