Hyperbolicity and GCD for n+1 divisors with non-empty intersection
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912963915415552 |
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| author | Wang, Julie Tzu-Yueh Xiao, Zheng |
| author_facet | Wang, Julie Tzu-Yueh Xiao, Zheng |
| contents | We study hyperbolicity for quasi-projective varieties where the boundary divisor consists of n+1 numerically parallel effective divisors on a complex projective variety of dimension n, allowing non-empty intersection. Under explicit local conditions on beta constants or intersection multiplicities, we prove that all entire curves are algebraically degenerate. Our approach extends the method of Levin-Huang-Xiao to higher dimensions, establishing a second main theorem for regular sequences of closed subschemes. This also yields a GCD-type estimate in the same geometric setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperbolicity and GCD for n+1 divisors with non-empty intersection Wang, Julie Tzu-Yueh Xiao, Zheng Complex Variables Number Theory We study hyperbolicity for quasi-projective varieties where the boundary divisor consists of n+1 numerically parallel effective divisors on a complex projective variety of dimension n, allowing non-empty intersection. Under explicit local conditions on beta constants or intersection multiplicities, we prove that all entire curves are algebraically degenerate. Our approach extends the method of Levin-Huang-Xiao to higher dimensions, establishing a second main theorem for regular sequences of closed subschemes. This also yields a GCD-type estimate in the same geometric setting. |
| title | Hyperbolicity and GCD for n+1 divisors with non-empty intersection |
| topic | Complex Variables Number Theory |
| url | https://arxiv.org/abs/2506.03534 |