The author thanks his co-authors on the various subjects treated in this paper. These include: Luis Alvarez-C´onsul, Steven Bradlow, Mario Garcia-Fernandez, Peter Gothen, Vamsi Pingali ´ and Chengjian Yao. He also thanks Jean-Pierre Bourguignon for comments and corrections on the first draft of this paper, and the IHES for its hospitality and support. Partially supported by the Spanish Ministry of Science and Innovation, through the “Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000904-S)” and PID2022-141387NB-C21.

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. © 2024, Institute of Mathematics. All rights reserved.

Peer reviewed