Stable reflexive sheaves. III
type: Item
instance of: scholarly article
title: Stable reflexive sheaves. III
zbMATH Open document ID: 0607.14009
DOI: 10.1007/BF01456285
author: Robin Hartshorne
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164338
review text: 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.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14H99
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 3981328
zbMATH Keywords: rank two stable reflexive sheaf
zbMATH Keywords: bound for the third Chern class
zbMATH Keywords: bound on genus of curves in projective 3-space
MaRDI profile type: Publication
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OpenAlex ID: W2090163387
description: scientific article; zbMATH DE number 3981328