2020/11/25 by Yanir A. Rubinstein, Kewei Zhang, Rubinstein, Yanir A. +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #math.DG
paper · pdf · doi:10.48550/arxiv.2011.12666
Final version, to appear in special issue in honor of Bernie Shiffman, Pure Appl. Math. Quart
openalex publication_date 2020/11/25 · arxiv created 2021/02/25 · arxiv updated 2021/02/26 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28
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.