The vortex equation on affine manifolds

2013/04/17 by Indranil Biswas, Biswas, Indranil, John Loftin +3 · 1 citation
Mathematics · #53C07 #57N16 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1304.4727

openalex publication_date 2013/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a compact connected special affine manifold equipped with an affine Gauduchon metric. We show that a pair (E, ϕ), consisting of a flat vector bundle E over M and a flat nonzero section ϕ of E, admits a solution to the vortex equation if and only if it is polystable. To prove this, we adapt the dimensional reduction techniques for holomorphic pairs on Kähler manifolds to the situation of flat pairs on affine manifolds.

Cited by

• Hermitian-Poisson metrics on projectively flat complex vector bundles over non-compact Gauduchon manifolds

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