Degenerations of the moduli spaces of vector bundles on curves. II. (Generalized Gieseker moduli spaces)
type: Item
instance of: scholarly article
title: Degenerations of the moduli spaces of vector bundles on curves. II. (Generalized Gieseker moduli spaces)
zbMATH Open document ID: 0957.14021
DOI: 10.1007/BF02841533
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2000-03-01T00:00:00Z
review text: For part I see \textit{D. S. Nagaraj} and \textit{C. S. Seshadri}, ibid. 107, No. 2, 101-137 (1997; Zbl 0922.14023). Let \(X_0\) be an irreducible projective curve of arithmetic genus \(g\geq 2\) whose singularity is one ordinary point. The authors give a generalisation of Gieseker's construction for arbitrary rank. They construct a birational model \(G(n,d)\) of the moduli space \(U(n,d)\) of stable torsion free sheaves in the case \((n,d)=1,\) such that \(G(n,d)\) has normal crossing singularities and behaves well under specialization, i.e. if a smooth projective curve specializes to \(X_0,\) then the moduli space of stable vector bundles of rank \(n\) and degree \(d\) on \(X\) specializes to \(G(n,d)\). This generalizes an earlier work of Gieseker in the rank two case. Theorem 1. There exists a canonical structure of a quasi-projective variety on \(G(n,d)\) and a canonical proper birational morphism \(\pi _{*}:G(n,d)\rightarrow U(n,d)_s\) onto the moduli space of stable torsion free sheaves on \(X_0.\) The singularities of \(G(n,d)\) are (analytic) normal crossings. If \((n,d)=1\), \(G(n,d)\) is projective, since \(U(n,d)_s=U(n,d)\) is projective.
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14D15
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14H20
zbMATH DE Number: 1348066
zbMATH Keywords: projective curves with singularities
zbMATH Keywords: moduli space of stable vector bundles
author: D. S. Nagaraj
author: Conjeevaram Srirangachari Seshadri
reviewed by: V. V. Chueshev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1348066