Coupled complex Monge-Amp\`ere equations on Fano horosymmetric manifolds
Abstract
We give necessary and sufficient conditions for existence of solutions to a general system of complex Monge-Amp\`ere equations on Fano horosymmetric manifolds. In particular, we get necessary and sufficient conditions for existence of coupled K\"ahler-Ricci solitons, Mabuchi metrics and twisted K\"ahler-Einstein metrics in terms of combinatorial data of the manifold.
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