Pure and Applied Mathematics Quarterly
Volume 15 (2019)
Special Issue in Honor of Simon Donaldson: Part 2 of 2
Guest Editor: Richard Thomas (Imperial College London)
On the Kähler–Yang–Mills–Higgs equations
Pages: 1181 – 1217
In this paper we introduce a set of equations on a principal bundle over a compact complex manifold coupling a connection on the principal bundle, a section of an associated bundle with Kähler fibre, and a Kähler structure on the base. These equations are a generalization of the Kähler–Yang–Mills equations introduced by the authors. They also generalize the constant scalar curvature for a Kähler metric studied by Donaldson and others, as well as the Yang–Mills–Higgs equations studied by Mundet i Riera. We provide a moment map interpretation of the equations, construct some first examples, and study obstructions to the existence of solutions.
The authors were partially supported by the Spanish MINECO under ICMAT Severo Ochoa project No. SEV-2015-0554, and under grant No. MTM2016-81048-P.
Received 22 June 2018
Published 20 March 2020