Journal of Symplectic Geometry

Volume 18 (2020)

Number 4

On coupled constant scalar curvature Kähler metrics

Pages: 961 – 994

DOI: https://dx.doi.org/10.4310/JSG.2020.v18.n4.a1

Authors

Ved V. Datar (Department of Mathematics, Indian Institute of Science, Bangalore, India)

Vamsi Pritham Pingali (Department of Mathematics, Indian Institute of Science, Bangalore, India)

Abstract

We provide a moment map interpretation for the coupled Kähler–Einstein equations introduced in [16], 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 Székelyhidi, 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.

Received 20 March 2019

Accepted 2 September 2019

Published 28 October 2020