Degenerations of Negative Kähler-Einstein Surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916132085039104 |
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| author | Mandel, Holly |
| author_facet | Mandel, Holly |
| contents | Every compact Kähler manifold with negative first Chern class admits a unique metric $g$ such that $\text{Ric}(g) = -g$. Understanding how families of these metrics degenerate gives insight into their geometry and is important for understanding the compactification of the moduli space of negative Kähler-Einstein metrics. I study a special class of such families in complex dimension two. Following the work of Sun and Zhang (2019) in the Calabi-Yau case, I construct a Kähler-Einstein neck region interpolating between canonical metrics on components of the central fiber. This provides a model for the limiting geometry of metrics in the family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_09792 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Degenerations of Negative Kähler-Einstein Surfaces Mandel, Holly Differential Geometry Every compact Kähler manifold with negative first Chern class admits a unique metric $g$ such that $\text{Ric}(g) = -g$. Understanding how families of these metrics degenerate gives insight into their geometry and is important for understanding the compactification of the moduli space of negative Kähler-Einstein metrics. I study a special class of such families in complex dimension two. Following the work of Sun and Zhang (2019) in the Calabi-Yau case, I construct a Kähler-Einstein neck region interpolating between canonical metrics on components of the central fiber. This provides a model for the limiting geometry of metrics in the family. |
| title | Degenerations of Negative Kähler-Einstein Surfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2206.09792 |