Quasi-projective manifolds uniformized by Carathéodory hyperbolic manifolds and hyperbolicity of their subvarieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913654587260928 |
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| author | Wong, Kwok-Kin Yeung, Sai-Kee |
| author_facet | Wong, Kwok-Kin Yeung, Sai-Kee |
| contents | Let $M$ be a Carathéodory hyperbolic complex manifold. We show that $M$ supports a real-analytic bounded strictly plurisubharmonic function. If $M$ is also complete Kähler, we show that $M$ admits the Bergman metric. When $M$ is strongly Carathéodory hyperbolic and is the universal covering of a quasi-projective manifold $X$, the Bergman metric can be estimated in terms of a Poincaré type metric on $X$. It is also proved that any quasi-projective (resp. projective) subvariety of $X$ is of log-general type (resp. general type), a result consistent with a conjecture of Lang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09922 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-projective manifolds uniformized by Carathéodory hyperbolic manifolds and hyperbolicity of their subvarieties Wong, Kwok-Kin Yeung, Sai-Kee Complex Variables 32Q45, 32Q40, 32U05 Let $M$ be a Carathéodory hyperbolic complex manifold. We show that $M$ supports a real-analytic bounded strictly plurisubharmonic function. If $M$ is also complete Kähler, we show that $M$ admits the Bergman metric. When $M$ is strongly Carathéodory hyperbolic and is the universal covering of a quasi-projective manifold $X$, the Bergman metric can be estimated in terms of a Poincaré type metric on $X$. It is also proved that any quasi-projective (resp. projective) subvariety of $X$ is of log-general type (resp. general type), a result consistent with a conjecture of Lang. |
| title | Quasi-projective manifolds uniformized by Carathéodory hyperbolic manifolds and hyperbolicity of their subvarieties |
| topic | Complex Variables 32Q45, 32Q40, 32U05 |
| url | https://arxiv.org/abs/2501.09922 |