English

Coupled equations for K\"ahler metrics and Yang-Mills connections

Differential Geometry 2016-01-20 v3 High Energy Physics - Theory Mathematical Physics Algebraic Geometry math.MP Symplectic Geometry

Abstract

We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki invariant, the Mabuchi K-energy and geodesic stability. We finish by giving some examples of solutions.

Keywords

Cite

@article{arxiv.1102.0991,
  title  = {Coupled equations for K\"ahler metrics and Yang-Mills connections},
  author = {Luis Alvarez-Consul and Mario Garcia-Fernandez and Oscar Garcia-Prada},
  journal= {arXiv preprint arXiv:1102.0991},
  year   = {2016}
}

Comments

61 pages; v2: introduction partially rewritten; minor corrections and improvements in presentation, especially in Section 4; added references; v3: To appear in Geom. Topol. Minor corrections and improvements, following comments by referees