Meromorphic maps from ${\Bbb C}^{p}$ into semi-abelian varieties and general projective varieties
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911311422554112 |
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| author | Wang, Zhe |
| author_facet | Wang, Zhe |
| contents | In 1953, W. Stoll proposed a method of studying holomorphic functions of several complex variables by reducing them to one variable through fiber integration. In this paper, we use this method to extend some important Nevanlinna-type results for holomorphic curves into projective varieties to meromorphic maps from ${\Bbb C}^{p}$ to projective varieties. This includes Bloch's theorem and Noguchi-Winklemann-Yamanoi's Second Main Theorem for holomorphic maps into semi-abelian varieties intersecting an effective divisor, as well as Huynh-Vu-Xie's Second Main Theorem for meromorphic maps into projective space intersecting with a generic hypersurface with sufficiently high degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Meromorphic maps from ${\Bbb C}^{p}$ into semi-abelian varieties and general projective varieties Wang, Zhe Complex Variables Algebraic Geometry In 1953, W. Stoll proposed a method of studying holomorphic functions of several complex variables by reducing them to one variable through fiber integration. In this paper, we use this method to extend some important Nevanlinna-type results for holomorphic curves into projective varieties to meromorphic maps from ${\Bbb C}^{p}$ to projective varieties. This includes Bloch's theorem and Noguchi-Winklemann-Yamanoi's Second Main Theorem for holomorphic maps into semi-abelian varieties intersecting an effective divisor, as well as Huynh-Vu-Xie's Second Main Theorem for meromorphic maps into projective space intersecting with a generic hypersurface with sufficiently high degree. |
| title | Meromorphic maps from ${\Bbb C}^{p}$ into semi-abelian varieties and general projective varieties |
| topic | Complex Variables Algebraic Geometry |
| url | https://arxiv.org/abs/2512.09805 |