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arXiv · 2011.12666

Angle deformation of K\"ahler-Einstein edge metrics on Hirzebruch surfaces

Yanir A. Rubinstein·Kewei Zhang
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Abstract

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.

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BibTeXRIS

Yanir A. Rubinstein, Kewei Zhang. 2020-11-25. Angle deformation of K\"ahler-Einstein edge metrics on Hirzebruch surfaces. https://arxiv.org/abs/2011.12666

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