Hyperbolicity and fundamental groups of complex quasi-projective varieties (I): Maximal quasi-Albanese dimension by Nevanlinna theory
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912691382124544 |
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| author | Cadorel, Benoit Deng, Ya Yamanoi, Katsutoshi |
| author_facet | Cadorel, Benoit Deng, Ya Yamanoi, Katsutoshi |
| contents | This is the first part of a series of three papers. In this paper, we establish a Big Picard type theorem for holomorphic maps $f:Y \to X$, where $Y$ is a ramified covering of the punctured disc $\mathbb{D}^*$ with small ramification and $X$ is a complex quasi-projective variety of log-general type and of maximal quasi-Albanese dimension. As a byproduct, we prove the generalized Green-Griffiths-Lang conjecture for such $X$. This paper summarizes the parts of the three-paper series that are based primarily on Nevanlinna theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperbolicity and fundamental groups of complex quasi-projective varieties (I): Maximal quasi-Albanese dimension by Nevanlinna theory Cadorel, Benoit Deng, Ya Yamanoi, Katsutoshi Algebraic Geometry Complex Variables This is the first part of a series of three papers. In this paper, we establish a Big Picard type theorem for holomorphic maps $f:Y \to X$, where $Y$ is a ramified covering of the punctured disc $\mathbb{D}^*$ with small ramification and $X$ is a complex quasi-projective variety of log-general type and of maximal quasi-Albanese dimension. As a byproduct, we prove the generalized Green-Griffiths-Lang conjecture for such $X$. This paper summarizes the parts of the three-paper series that are based primarily on Nevanlinna theory. |
| title | Hyperbolicity and fundamental groups of complex quasi-projective varieties (I): Maximal quasi-Albanese dimension by Nevanlinna theory |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2511.04405 |