全纯扩展

Advances in Mathematics: Scientific Journal Pub Date : 2023-01-23 DOI:10.37418/amsj.12.1.14

M.N. Boukhetouta, M. Krachni, F. Yazid, F.S. Djeradi

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引用次数: 0

摘要

在本文中，我们证明了如果存在一个定义在复流形$ X $上的全纯的、固有的满射映射到具有可并行纤维的光滑代数曲线上，那么定义在$\mathbb{C}^n$的Hartogs定域$ T $上的任何全纯映射都可以被全纯扩展。亚纯地)从$\Delta^n \set - Z $变成$ X $，其中$ Z $是$\Delta^n $的解析子集，使得$ Z $的余维至少为2。

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HOLOMORPHIC EXTENSION

In this paper, we prove that if there exists a holomorphic, proper, surjective map defined on a complex manifold $ X $ into a smooth algebraic curve with parallelizable fibers, then any holomorphic mappings defined on the Hartogs domain $ T $ of $\mathbb{C}^n$ can be extended holomorphically (resp. meromorphically) from $ \Delta ^n \setminus Z $ into $ X $, where $ Z $ is an analytic subset of $\Delta^n $ such that codimension of $ Z $ at least 2.

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Advances in Mathematics: Scientific Journal

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