Moduli spaces of holomorphic triples over compact Riemann surfaces
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 nonemptiness, 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, which we explore in a companion paper "Surface group representations in PU(p,q) and Higgs bundles". 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. This paper, and its companion mentioned above, form a substantially revised version of math.AG/0206012.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2002
 arXiv:
 arXiv:math/0211428
 Bibcode:
 2002math.....11428B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Differential Geometry;
 14D20 (Primary) 14H60;
 32G13 (Secondary)
 EPrint:
 44 pages. v2: minor clarifications and corrections, to appear in Math. Annalen