Moduli of parabolic stable sheaves on a projective scheme
type: Item
instance of: scholarly article
title: Moduli of parabolic stable sheaves on a projective scheme
zbMATH Open document ID: 1002.14002
author: Michi-Aki Inaba
published in: Journal of Mathematics of Kyoto University
publication date: 2000-11-13T00:00:00Z
review text: Let \(X\) be a smooth projective variety. A parabolic bundle on \(X\) consists of a pair \(f:E\to F\), where \(E\) is a locally free sheaf on \(X\), \(F\) is a torsion sheaf on \(X\) and \(f\) is surjective. There is a notion of stability of such pairs, and a moduli space of such pairs was constructed before. In this article, the author considers a more general class of parabolic sheaves. The parabolic sheaves are still pairs \(f:E\to F\). However, in this case the base scheme \(X\) can be any projective scheme, the sheaf \(E\) is only assumed to be of pure dimension \(d\) and \(f\) is still surjective. The author then introduces the stability notion for such pairs, based on the Simpson stability of sheaves of pure dimension. The author proves that there is a coarse moduli scheme for parabolic sheaves on any projective scheme.
reviewed by: Jun Li
Mathematics Subject Classification ID: 14D22
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 1502030
zbMATH Keywords: coarse moduli scheme
zbMATH Keywords: parabolic sheaves
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250517762
OpenAlex ID: W1521787865
DOI: 10.1215/KJM/1250517762
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description: scientific article; zbMATH DE number 1502030