Abstract
We show that there exist Kähler–Einstein metrics on two exceptional Pasquier’s two-orbits varieties. As an application, we will provide a new example of K-unstable Fano manifold with Picard number one.
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Acknowledgements
The author wishes to express his gratitude to Professor Thibaut Delcroix for careful reading of the first draft of this paper, and also for discussions about the difference between his proof and our proof. The author is also grateful to Professors Kento Fujita and Yuji Odaka for helpful discussions and also for answering questions on K-stability of Fano varieties. The author also would like to thank Professor Baohua Fu for drawing his attention to [3] and for explaining Remark 5.3.
Funding
The author was a JSPS Research Fellow and supported by the Grant-in-Aid for JSPS fellows (JSPS KAKENHI Grant Number 18J00681).
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Kanemitsu, A. Kähler–Einstein metrics on Pasquier’s two-orbits varieties. manuscripta math. 169, 297–311 (2022). https://doi.org/10.1007/s00229-021-01338-y
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DOI: https://doi.org/10.1007/s00229-021-01338-y