Gaps in Chern classes of rank 2 stable reflexive sheaves
type: Item
instance of: scholarly article
title: Gaps in Chern classes of rank 2 stable reflexive sheaves
zbMATH Open document ID: 0535.14010
DOI: 10.1007/BF01473429
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/182961
review text: The paper contains the characterization of the set of integers \(c_ 1\), \(c_ 2\), \(c_ 3\) such that there is a rank 2 stable reflexive sheaf on \({\mathbb{P}}^ 3\) whose Chern classes are \(c_ 1\), \(c_ 2\), \(c_ 3\). This answers a question of \textit{R. Hartshorne} [Math. Ann. 254, 121-176 (1980; Zbl 0431.14004)]. The proof consists of two parts. First of all, using the well known correspondence between curves of \({\mathbb{P}}^ 3\) and rank 2 reflexive sheaves, we construct some families of rank 2 reflexive sheaves and we analyse which values of \(c_ 1\), \(c_ 2\), \(c_ 3\) appear. Then we prove that the undecided cases are indeed non-existent.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 55R20
zbMATH DE Number: 3849395
zbMATH Keywords: rank 2 stable reflexive sheaf with prescribed Chern classes
author: Rosa M. Miró-Roig
MaRDI profile type: Publication
cites work: Vector bundles on projective 3-spaces
cites work: Stable rank 2 reflexive sheaves on with large c3
cites work: Stable reflexive sheaves. II
cites work: Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
cites work: Stable vector bundles of rank 2 on \(P^ 3\)
description: scientific article; zbMATH DE number 3849395