Residue formula for an obstruction to coupled Kahler-Einstein metrics

摘要

We obtain a residue formula for an obstruction to the existence of coupled Kahler-Einstein metrics described by Futaki-Zhang. We apply it to an example studied separately by Futaki and Hultgren which is a toric Fano manifold with reductive automorphism, does not admit a Kahler-Einstein metric but still admits coupled Kahler-Einstein metrics.