On the uniqueness of the Horrocks-Mumford-bundle
type: Item
instance of: scholarly article
title: On the uniqueness of the Horrocks-Mumford-bundle
zbMATH Open document ID: 0598.14013
DOI: 10.1007/BF01450731
author: W. Decker
author: Frank-Olaf Schreyer
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164066
review text: In this paper the authors show that there is only one stable \(rank\quad 2\) bundle \({\mathcal F}\) on \({\mathbb{P}}^ 4\) with Chern classes \(c_ 1=-1\), \(c_ 2=4\) and \(H^ 2({\mathbb{P}}_ 4,{\mathcal F}(-1))=0\). The vanishing of \(H^ 2\) can be omitted according to a result announced by Lipschitz and to appear in a paper by W. Decker. The result is proved by studying the variety of unstable planes and showing that it is a smooth surface fibred over \({\mathbb{P}}_ 1\) by elliptic curves. The singular fibres are pentagons and these give rise to the standard monad on \({\mathbb{P}}^ 4\).
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 3964012
zbMATH Keywords: uniqueness of the Horrocks-Mumford-bundle
zbMATH Keywords: variety of unstable planes
zbMATH Keywords: standard monad
reviewed by: G. Horrocks
MaRDI profile type: Publication
cites work: Q3347989
cites work: Generic free resolutions and a family of generically perfect ideals
cites work: Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
cites work: Coherent sheaves on \({\mathbb{P}}^n\) and problems of linear algebra
cites work: Q5749404
cites work: Ideals defined by matrices and a certain complex associated with them
cites work: Q3919817
cites work: A rank 2 vector bundle on P\(^4\) with 15,000 symmetries
cites work: Moduli of stable sheaves. II
cites work: Vector bundles on complex projective spaces
cites work: On elliptic modular surfaces
description: scientific article; zbMATH DE number 3964012