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Residue formula for an obstruction to coupled Kähler–Einstein metrics

Akito Futaki Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China Yingying Zhang Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China

Differential Geometry mathscidoc:2204.10004

The Mathematical Society of Japan, 73, (2), 2021.4
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.
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@inproceedings{akito2021residue,
  title={Residue formula for an obstruction to coupled Kähler–Einstein metrics},
  author={Akito Futaki, and Yingying Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428135013244602140},
  booktitle={The Mathematical Society of Japan},
  volume={73},
  number={2},
  year={2021},
}
Akito Futaki, and Yingying Zhang. Residue formula for an obstruction to coupled Kähler–Einstein metrics. 2021. Vol. 73. In The Mathematical Society of Japan. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428135013244602140.
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