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On coupled constant scalar curvature Kähler metrics
Journal of Symplectic Geometry  (IF0.707),  Pub Date : 2020-01-01, DOI: 10.4310/jsg.2020.v18.n4.a1
Ved V. Datar, Vamsi Pritham Pingali

We provide a moment map interpretation for the coupled K\"ahler-Einstein equations introduced by Hultgren and Witt Nystr\"om, and in the process introduce a more general system of equations, which we call coupled cscK equations. A differentio-geometric formulation of the corresponding Futaki invariant is obtained and a notion of K-polystability is defined for this new system. Finally, motivated by a result of Sz\'ekelyhidi, we prove that if there is a solution to our equations, then small K-polystable perturbations of the underlying complex structure and polarizations also admit coupled cscK metrics.