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Angle deformation of Kähler-Einstein edge metrics on Hirzebruch surfaces

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.

preprint2021arXivOpen access
Yanir A. RubinsteinKewei Zhang
math.AGmath.DG
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Yanir A. RubinsteinKewei Zhang

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