Angle deformation of K\"ahler-Einstein edge metrics on Hirzebruch surfaces.
2020
We construct a family of K\"ahler-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 K\"ahler-Einstein edge metric whose edge singularity is rigid, answering a question posed by Cheltsov.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
11
References
1
Citations
NaN
KQI