On uniform log $K$-stability for constant scalar curvature Kähler cone metrics
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| Format: | Preprint |
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2021
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| _version_ | 1866914101065678848 |
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| author | Aoi, Takahiro Hashimoto, Yoshinori Zheng, Kai |
| author_facet | Aoi, Takahiro Hashimoto, Yoshinori Zheng, Kai |
| contents | We prove that the existence of constant scalar curvature Kähler metrics with cone singularities along a divisor implies log $K$-polystability and $G$-uniform log $K$-stability, where $G$ is the automorphism group which preserves the divisor. We also show that a constant scalar curvature Kähler cone metric along an ample divisor of sufficiently large degree always exists. We further show several properties of the path of constant scalar curvature Kähler cone metrics and discuss uniform log $K$-stability of normal varieties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2110_02518 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On uniform log $K$-stability for constant scalar curvature Kähler cone metrics Aoi, Takahiro Hashimoto, Yoshinori Zheng, Kai Differential Geometry Algebraic Geometry Analysis of PDEs Complex Variables 53C55 (Primary), 32Q26 (Secondary) We prove that the existence of constant scalar curvature Kähler metrics with cone singularities along a divisor implies log $K$-polystability and $G$-uniform log $K$-stability, where $G$ is the automorphism group which preserves the divisor. We also show that a constant scalar curvature Kähler cone metric along an ample divisor of sufficiently large degree always exists. We further show several properties of the path of constant scalar curvature Kähler cone metrics and discuss uniform log $K$-stability of normal varieties. |
| title | On uniform log $K$-stability for constant scalar curvature Kähler cone metrics |
| topic | Differential Geometry Algebraic Geometry Analysis of PDEs Complex Variables 53C55 (Primary), 32Q26 (Secondary) |
| url | https://arxiv.org/abs/2110.02518 |