Chern classes of rank 3 stable reflexive sheaves
type: Item
instance of: scholarly article
title: Chern classes of rank 3 stable reflexive sheaves
zbMATH Open document ID: 0588.14011
DOI: 10.1007/BF01450743
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164198
review text: The paper contains the characterization of the set of integers \(c_ 1, c_ 2, c_ 3\) such that there exists a rank 3 stable reflexive sheaf on \({\mathbb{P}}^ 3\) with Chern classes \(c_ 1, c_ 2\) and \(c_ 3\). The proof consists of two parts. First of all, we construct some good families of rank 3 stable reflexive sheaves on \({\mathbb{P}}^ 3\) and we analyze which values of \(c_ 1, c_ 2\) and \(c_ 3\) appear. Then we prove that the undecided cases are indeed non-existent. The characterization of the triples \((c_ 1,c_ 2,c_ 3)\in {\mathbb{Z}}^ 3\) such that there exists a rank 3 stable reflexive sheaf E on \({\mathbb{P}}^ 3\) with \(c_ iE=c_ i\) is a step toward the problem of characterizing the 4-uples \((c_ 1,c_ 2,c_ 3,s)\in {\mathbb{Z}}^ 4\) such that there exists a rank 3 stable reflexive sheaf E on \({\mathbb{P}}^ 3\) with \(c_ iE=c_ i\) and having s singular points. For \(s=0\), this problem amounts to characterizing the Chern classes of rank 3 stable vector bundles on \({\mathbb{P}}^ 3\), settled recently by \textit{I. Coandă} [Math. Ann. 273, 65-79 (1985; see the preceding review)].
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 3944012
zbMATH Keywords: rank 3 stable reflexive sheaf on projective 3-space
zbMATH Keywords: Chern classes
author: Rosa M. Miró-Roig
MaRDI profile type: Publication
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OpenAlex ID: W80378475
description: scientific article; zbMATH DE number 3944012