A continuous cusp closing process for negative Kähler-Einstein metrics
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929657846169600 |
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| author | Fu, Xin Hein, Hans-Joachim Jiang, Xumin |
| author_facet | Fu, Xin Hein, Hans-Joachim Jiang, Xumin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11468 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A continuous cusp closing process for negative Kähler-Einstein metrics Fu, Xin Hein, Hans-Joachim Jiang, Xumin Differential Geometry 53C25, 32Q20 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. |
| title | A continuous cusp closing process for negative Kähler-Einstein metrics |
| topic | Differential Geometry 53C25, 32Q20 |
| url | https://arxiv.org/abs/2401.11468 |