Residue formula for an obstruction to Coupled Kähler-Einstein metrics

Abstract

We obtain a residue formula for an obstruction to the existence of coupled Kähler-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 Kähler-Einstein metric but still admits coupled Kähler-Einstein metrics.

10 pages