Mathematische Annalen

, Volume 328, Issue 1–2, pp 299–351 | Cite as

Moduli spaces of holomorphic triples over compact Riemann surfaces

  • Steven B. BradlowEmail author
  • Oscar Gar-cía-Prada
  • Peter B. Gothen


A holomorphic triple over a compact Riemann surface consists of two holomorphic vector bundles and a holomorphic map between them. After fixing the topological types of the bundles and a real parameter, there exist moduli spaces of stable holomorphic triples. In this paper we study non-emptiness, irreducibility, smoothness, and birational descriptions of these moduli spaces for a certain range of the parameter. Our results have important applications to the study of the moduli space of representations of the fundamental group of the surface into unitary Lie groups of indefinite signature ([5, 7]). Another application, that we study in this paper, is to the existence of stable bundles on the product of the surface by the complex projective line.


Modulus Space Vector Bundle Riemann Surface Fundamental Group Important Application 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Steven B. Bradlow
    • 1
    Email author
  • Oscar Gar-cía-Prada
    • 2
  • Peter B. Gothen
    • 3
  1. 1.Department of MathematicsUniversity of IllinoisUSA
  2. 2.Instituto de Matemáticas y Física FundamentalConsejo Superior de Investigaciones CientíficasMadridSpain
  3. 3.Departamento de Matemática PuraFaculdade de CiênciasPortugal

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