Generic fibres on the projective plane
type: Item
instance of: scholarly article
title: Generic fibres on the projective plane
zbMATH Open document ID: 0808.14007
DOI: 10.1007/BF01459489
author: Yves Laszlo
author: André Hirschowitz
published in: Mathematische Annalen
publication date: 1995-03-09T00:00:00Z
full work available at URL: https://eudml.org/doc/165119
review text: The main result of this paper is a new proof of the irreducibility of the moduli spaces of stable vector bundles over the projective plane. Until now this study was done in four separate cases: (1) \(c_ 1 = 0\), \(\text{rk} = 2\) (W. Barth (1977)); (2) \(c_ 1 = - 1\), \(\text{rk} = 2\) (K. Hulek (1979) und G. Ellingsrud, S. A. Stromme (1979)); (3) \(c_ 1 = 0\), \(\text{rk} \geq 3\) (K. Hulek (1980)), (4) the remaining cases (G. Ellingsrud (1983)). Here the irreducibility follows from the general result that ``le champ'' (in the sense of G. Laumon, L. Moret-Baily) of ``prioritaire'' sheaves with fixed Hilbert polynomial is irreducible.
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J60
zbMATH DE Number: 537200
zbMATH Keywords: Chern classes
zbMATH Keywords: irreducibility of the moduli spaces of stable vector bundles
zbMATH Keywords: Hilbert polynomial
reviewed by: Nicolae Manolache
MaRDI profile type: Publication
cites work: Moduli of vector bundles on the projective plane
cites work: Q3220676
cites work: Sur l'irréductibilité du module des fibres stables sur \(P_ 2\)
cites work: Stable rank-2 vector bundles on \(\mathbb{P}_2\) with \(c_1\) odd
cites work: Q4935967
cites work: Stable vector bundles on an algebraic surface
description: scientific article; zbMATH DE number 537200