Generalized parabolic bundles and applications. II
type: Item
instance of: scholarly article
title: Generalized parabolic bundles and applications. II
zbMATH Open document ID: 0879.14012
DOI: 10.1007/BF02837696
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1998-01-25T00:00:00Z
review text: The author further develops her theory of generalized parabolic bundles (vector bundles with flags of vector spaces over effective divisors) on smooth curves, initiated in part I of this paper [\textit{U. N. Bhosle}, Ark. Mat. 30, No. 2, 187-215 (1992; Zbl 0773.14006)]. In that paper, she considered the special case of flags of length 2. In the paper under review, the author considers flags of sufficiently general type and proves the existence of the moduli space \(M(n,d)\) of semistable generalized parabolic bundles of rank \(n\) and degree \(d\). She studies some interesting cases of such moduli spaces and finds explicit geometric descriptions for them in low ranks and genera. The author also defines the subvariety \(M_L (n,d)\) corresponding to the semistable generalized parabolic bundles with fixed determinant \(L\), where \(L\) is a generalized parabolic bundle of rank 1. She applies her results to the study of moduli spaces of torsion free sheaves on a reduced irreducible curve with nodes and ordinary cusps as singularities.
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14D20
zbMATH DE Number: 1043989
zbMATH Keywords: nodal curves
zbMATH Keywords: torsion free sheaves
zbMATH Keywords: generalized parabolic bundles
zbMATH Keywords: flags of vector spaces
zbMATH Keywords: moduli spaces
Wikidata QID: Q57406336
author: Usha N. Bhosle
reviewed by: Iustin Coandă
MaRDI profile type: Publication
cites work: On the ubiquity of Gorenstein rings
cites work: Parabolic vector bundles on curves
cites work: Parabolic sheaves on higher dimensional varieties
cites work: Generalised parabolic bundles and applications to torsionfree sheaves on nodal curves
cites work: Representations of the fundamental group and vector bundles
cites work: Q4863641
cites work: Q4260730
cites work: Q3884235
cites work: On the moduli of vector bundles on an algebraic surface
cites work: Q3871006
cites work: Lectures on introduction to moduli problems and orbit spaces
cites work: Compactification of the space of vector bundles on a singular curve
cites work: Factorisation of generalised theta functions. I
cites work: Orthogonal and spin bundles over hyperelliptic curves
cites work: Q3665240
cites work: Moduli of vector bundles on curves with parabolic structures
description: scientific article; zbMATH DE number 1043989