Moduli spaces of holomorphic triples over compact Riemann surfaces

Steven B. Bradlow, Oscar García-Prada, Peter B. Gothen

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)299-351
Number of pages53
JournalMathematische Annalen
Volume328
Issue number1-2
DOIs
StatePublished - Jan 2004

ASJC Scopus subject areas

  • General Mathematics

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