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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.07382 |
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| _version_ | 1866916318409654272 |
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| author | Zhang, Junsheng |
| author_facet | Zhang, Junsheng |
| contents | Let $(Z,p)$ be a pointed Gromov-Hausdorff limit of non-collapsing Kähler-Einstein metrics with uniformly bounded Ricci curvature. We show that the singular Kähler-Einstein metric on $Z$ is conical at $p$ if and only if $\mathcal C=W$ in Donaldson-Sun's two-step degeneration theory, assuming curvature grows at most quadratically near $p$.
Let $(X,p)$ be a germ of an isolated log terminal algebraic singularity. Following Hein-Sun's approach, we show that if $\mathcal C=W$ in the two-step stable degeneration of $(X,p)$ and $\mathcal C$ has a smooth link, then every singular Kähler-Einstein metric on $X$ with non-positive Ricci curvature and bounded potential is conical at $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On polynomial convergence to tangent cones for singular Kähler-Einstein metrics Zhang, Junsheng Differential Geometry Let $(Z,p)$ be a pointed Gromov-Hausdorff limit of non-collapsing Kähler-Einstein metrics with uniformly bounded Ricci curvature. We show that the singular Kähler-Einstein metric on $Z$ is conical at $p$ if and only if $\mathcal C=W$ in Donaldson-Sun's two-step degeneration theory, assuming curvature grows at most quadratically near $p$. Let $(X,p)$ be a germ of an isolated log terminal algebraic singularity. Following Hein-Sun's approach, we show that if $\mathcal C=W$ in the two-step stable degeneration of $(X,p)$ and $\mathcal C$ has a smooth link, then every singular Kähler-Einstein metric on $X$ with non-positive Ricci curvature and bounded potential is conical at $p$. |
| title | On polynomial convergence to tangent cones for singular Kähler-Einstein metrics |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2407.07382 |