RCD structures on singular Kahler spaces of complex dimension three
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917952088965120 |
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| author | Fu, Xin Guo, Bin Song, Jian |
| author_facet | Fu, Xin Guo, Bin Song, Jian |
| contents | Let X be a projective variety of complex dimension 3 with log terminal singularities. We prove that every singular Kahler metric on X with bounded Nash entropy and Ricci curvature bounded below induces a compact RCD space homeomorphic to the projective variety X itself. In particular, singular Kahler-Einstein spaces of complex dimension 3 with bounded Nash entropy are compact RCD spaces topologically and holomorphically equivalent to the underlying projective variety. Various compactness theorems are also obtained for 3-dimensional projective varieties with bounded Ricci curvature. Such results establish connections among algebraic, geometric and analytic structures of klt singularities from birational geometry and provide abundant examples of RCD spaces from algebraic geometry via complex Monge-Ampere equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | RCD structures on singular Kahler spaces of complex dimension three Fu, Xin Guo, Bin Song, Jian Differential Geometry Algebraic Geometry Analysis of PDEs Let X be a projective variety of complex dimension 3 with log terminal singularities. We prove that every singular Kahler metric on X with bounded Nash entropy and Ricci curvature bounded below induces a compact RCD space homeomorphic to the projective variety X itself. In particular, singular Kahler-Einstein spaces of complex dimension 3 with bounded Nash entropy are compact RCD spaces topologically and holomorphically equivalent to the underlying projective variety. Various compactness theorems are also obtained for 3-dimensional projective varieties with bounded Ricci curvature. Such results establish connections among algebraic, geometric and analytic structures of klt singularities from birational geometry and provide abundant examples of RCD spaces from algebraic geometry via complex Monge-Ampere equations. |
| title | RCD structures on singular Kahler spaces of complex dimension three |
| topic | Differential Geometry Algebraic Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2503.08865 |