Angle deformation of K\"ahler-Einstein edge metrics on Hirzebruch surfaces
Differential Geometry
2021-02-26 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2011.12666,
title = {Angle deformation of K\"ahler-Einstein edge metrics on Hirzebruch surfaces},
author = {Yanir A. Rubinstein and Kewei Zhang},
journal= {arXiv preprint arXiv:2011.12666},
year = {2021}
}
Comments
Final version, to appear in special issue in honor of Bernie Shiffman, Pure Appl. Math. Quart