Non-simple semistable vector bundles over a curve
type: Item
instance of: scholarly article
title: Non-simple semistable vector bundles over a curve
zbMATH Open document ID: 0790.14018
DOI: 10.1007/BF02571660
published in: Mathematische Zeitschrift
publication date: 1994-06-20T00:00:00Z
full work available at URL: https://eudml.org/doc/174489
review text: Let \(X\) be a nonsingular algebraic curve over \(\mathbb{C}\) of genus \(g\geq 2\). Let \(S(3,0)\) be the set of indecomposable semistable vector bundles over \(X\) of rank 3 and degree 0. The nonsimple vector bundles in \(S(3,0)\) must have their algebra of endomorphisms isomorphic to \(\mathbb{C}[t]/(t^ 2)\), \(\mathbb{C}[t]/(t^ 3)\) or \(\mathbb{C}[r,s]/(r,s)^ 2\). We shall prove that if we fix the algebra of endomorphisms then there exists a moduli space \(M_ i\) for such vector bundles in \(S(3,0)\). For some \(i\), \(M_ i\) is a fine moduli space, i.e. there exists a universal family parametrized by \(M_ i\). Mainly we use the universal extensions of families of vector bundles over \(X\) and we prove that under a suitable equivalence relation these extensions define the required moduli spaces.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14D22
zbMATH DE Number: 549758
zbMATH Keywords: algebraic curve
zbMATH Keywords: semistable vector bundles
zbMATH Keywords: endomorphisms
zbMATH Keywords: fine moduli space
author: L. Brambila-Paz
MaRDI profile type: Publication
cites work: Algebras of endomorphisms of semistable vector bundles of rank 3 over a Riemann surface
cites work: Moduli of endomorphisms of semistable vector bundles over a compact Riemann surface
cites work: Topics in Algebraic and Analytic Geometry. (MN-13): Notes From a Course of Phillip Griffiths
cites work: Produits tensoriels topologiques et espaces nucléaires
cites work: Universal families of extensions
cites work: Cohomologie de la grassmannienne à valeurs dans les puissances extérieurs et symétriques du fibre universel
cites work: Moduli of vector bundles on a compact Riemann surface
cites work: Deformations of the moduli space of vector bundles over an algebraic curve
cites work: Stable and unitary vector bundles on a compact Riemann surface
OpenAlex ID: W1977769378
description: scientific article; zbMATH DE number 549758