Pure and Applied Mathematics Quarterly
Volume 18 (2022)
Special Issue in Honor of Bernie Shiffman
Guest Editors: Yuan Yuan, Christopher Sogge, and Steven Morris Zelditch
Angle deformation of Kähler–Einstein edge metrics on Hirzebruch surfaces
Pages: 343 – 366
We construct a family of Kähler–Einstein edge metrics on all Hirzebruch surfaces using the Calabi ansatz and study their angle deformation. This allows us to verify in some special cases a conjecture of Cheltsov–Rubinstein that predicts convergence towards a non-compact Calabi–Yau fibration in the small angle limit. We also give an example of a Kähler–Einstein edge metric whose edge singularity is rigid, answering a question posed by Cheltsov.
Kähler–Einstein edge metric, Calabi–Yau fiberation
2010 Mathematics Subject Classification
Primary 32Q20, 53C25. Secondary 32Q26.
Received 5 July 2020
Accepted 24 November 2020
Published 10 February 2022