Work

A Continuous Cusp Closing Process for Negative Kähler-Einstein Metrics

Year: 2025

Type: article

Abstract: We give an example of a family of smooth complex algebraic surfaces of degree 6 in $\mathbb{CP}^{3}$ developing an isolated elliptic singularity. We show via a gluing construction that the unique Kähler-Einstein metrics of Ricci curvature −1 on these sextics develop a complex hyperbolic cusp in the limit, and that near the tip of the forming cusp a Tian-Yau gravitational instanton bubbles off.

Source: Geometric and Functional Analysis

DOI: 10.1007/s00039-025-00708-y

Authors: Xin Fu, Hans-Joachim Hein, Xumin Jiang

Institutions: Westlake University, University of Münster, Great Bay University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,390

Funder: Westfälische Wilhelms-Universität Münster