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Holomorphic Maps from ℂp into Semi-Abelian Varieties
Abstract
We prove the Second Main Theorem with truncation level one for holomorphic maps with Zariski-dense image intersecting a reduced effective Cartier divisor: Let A be a semi-abelian variety with an equivariant compactification A⊂A̅, and let f:ℂp→ A be a holomorphic map with Zariski-dense image. Let D be a reduced effective divisor on A extending to a divisor D̅ on A̅. After possibly replacing A̅ by another equivariant compactification depending only on D and independent of f, for every ε>0, Tf(r,D̅)≤excNf[1](r,D)+ε Tf(r,D̅).
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BibTeX
@misc{wang2026holomorphic,
title = {{Holomorphic Maps from $\mathbbC^p$ into Semi-Abelian Varieties}},
author = {Zhe Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05768},
eprint = {2609.05768},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05768},
}
RIS
TY - UNPB
TI - Holomorphic Maps from ℂ^p into Semi-Abelian Varieties
AU - Zhe Wang
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.05768
UR - https://arxiv.org/abs/2609.05768
AB - We prove the Second Main Theorem with truncation level one for holomorphic maps with Zariski-dense image intersecting a reduced effective Cartier divisor: Let A be a semi-abelian variety with an equivariant compactification A⊂A̅, and let f:ℂ^p→ A be a holomorphic map with Zariski-dense image. Let D be a reduced effective divisor on A extending to a divisor D̅ on A̅. After possibly replacing A̅ by another equivariant compactification depending only on D and independent of f, for every ε>0, T_f(r,D̅)≤_excN_f^[1](r,D)+ε T_f(r,D̅).
ER -