Kähler-Yang-Mills Equations and Vortices

Abstract

The Kähler-Yang-Mills equations are coupled equations for a Kähler metric on a compact complex manifold and a connection on a complex vector bundle over it. After briefly reviewing the main aspects of the geometry of the Kähler-Yang-Mills equations, we consider dimensional reductions of the equations related to vortices - solutions to certain Yang-Mills-Higgs equations.

arXiv commentPaper in honour of Jean-Pierre Bourguignon

References in corpus (6)

• Surface group representations in PU(p,q) and Higgs bundles
• Moduli spaces of holomorphic triples over compact Riemann surfaces
• The y-genus of the moduli space of PGL_n-Higgs bundles on a curve (for degree coprime to n)
• Coupled equations for Kähler metrics and Yang-Mills connections
• Moduli of polarised manifolds via canonical Kähler metrics
• Deformations of complex structures and the coupled Kähler-Yang-Mills equations