We will continue the Coupled Kähler-Einstein and Yang-Mills equations. We will consider some examples of solutions of coupled KEYM equations (trivial and non-trivial). If time permits, we will introduce a Futaki type obstruction.
Kähler-Einstein equation, Yang-Mills equation and Moment map
References:


[ACGFGP13]     Luis Álvarez Cónsul, Mario Garíca-Fernández, and Oscar Garíca-Prada. Coupled equations for Kähler metrics and Yang-Mills connections. Geom. Topol., 17(5):2731-2812, 2013.

[Don17]     S. K. Donaldson. The Ding functional, Berndtsson convexity and moment maps. In Geometry, analysis and probability, volume 310 of Progr. Math., pages 57-67. Birkhäuser/Springer, Cham, 2017.
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