2002/06/03 by Steven B. Bradlow, Bradlow, Steven B., Oscar Garcia-Prada +4 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #math.AG #math.DG
paper · pdf · doi:10.48550/arxiv.math/0206003
38 pages
arxiv created 2002/06/03 · openalex publication_date 2002/06/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A principal pair consists of a holomorphic principal G-bundle together with a holomorphic section of an associated Kaehler fibration. Such objects support natural gauge theoretic equations coming from a moment map condition, and also admit a notion of stability based on Geometric Invariant Theory. The Hitchin--Kobayashi correspondence for principal pairs identifies stability as the condition for the existence of solutions to the equations. In this paper we generalize these features in a way which allows the full gauge group of the principal bundle to be replaced by certain proper subgroups. Such a generalization is needed in order to use principal pairs as a general framework for describing augmented holomorphic bundles. We illustrate our results with applications to well known examples.