Moduli spaces of holomorphic triples over compact Riemann surfaces

• Type: Article in International Scientific Journal
• Date: 2004

Authors

Bradlow, SB (Author) Other; Garcia Prada, O (Author) Other; Gothen, PB (Author) FCUP

Journal

Title: Mathematische Annalen

Vol. 328

Pages: 299-351

ISSN: 0025-5831

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 42 Citations

Scopus - 48 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-D6Z

DOI: 10.1007/s00208-003-0484-z

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 53