负Kähler-Einstein指标的连续尖峰关闭过程

IF 2.4 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis Pub Date : 2025-03-04 DOI:10.1007/s00039-025-00708-y

Xin Fu, Hans-Joachim Hein, Xumin Jiang

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引用次数: 0

摘要

我们给出了在\(\mathbb{CP}^{3}\)上的一类6次光滑复代数曲面发展孤立椭圆奇点的例子。我们通过粘接构造证明了这些结构上Ricci曲率- 1的独特Kähler-Einstein度量在极限处形成一个复杂的双曲尖峰，并且在形成尖峰的尖端附近产生了一个天丘引力瞬子气泡。

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A Continuous Cusp Closing Process for Negative Kähler-Einstein Metrics

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.

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来源期刊

Geometric and Functional Analysis 数学-数学

CiteScore

3.70

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.