Compactification of the moduli spaces of vortices and coupled vortices

2002/03/08 by Gang Tian, Tian, Gang, Baozhong Yang +1 · 1 citation
Mathematics · Physics and Astronomy · #32L17 #53C07 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons #math.AG #math.DG #msc:32L17 #msc:53C07

paper · pdf · doi:10.48550/arxiv.math/0203078

24 pages

arxiv created 2002/03/08 · openalex publication_date 2002/03/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Vortices and coupled vortices arise from Yang-Mills-Higgs theories and can be viewed as generalizations or analogues to Yang-Mills connections and, in particular, Hermitian-Yang-Mills connections. We proved an analytic compactification of the moduli spaces of vortices and coupled vortices on hermitian vector bundles over compact Kähler manifolds. In doing so we introduced the concept of ideal coupled vortices and characterized the singularities of ideal coupled vortices as well as Hermitian-Yang-Mills connections.

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