强支配性准则与Oka并集定理
A Strong Dominability Criterion and an Oka Union Theorem
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中文总结 AI 辅助
本文提出强可支配性等价于Oka性质的准则，并证明Oka性质可跨越真闭复解析子集延拓，为构造新Oka流形提供了有力工具。
中文摘要 AI 辅助
我们证明了一个$n$维复流形$Y$是Oka流形当且仅当它是强可支配的：对于每个$y\in Y$，存在一个整映射$F:\mathbb{C}^n\to Y$使得$F(0)=y$且$dF_0$可逆。该论证将此逐点支配性转化为所有源维度中的凸逼近性质。我们还证明了Oka性质在真闭复解析子集上可延拓：若$A$是连通复流形$X$的这样的子集，且$X\setminus A$是Oka流形，则$X$也是Oka流形。该准则具有广泛的应用，并产生了许多新的Oka流形例子。
英文摘要
We prove that an $n$-dimensional complex manifold $Y$ is Oka if and only if it is strongly dominable: for every $y\in Y$, there is an entire map $F:\mathbb{C}^n\to Y$ such that $F(0)=y$ and $dF_0$ is invertible. The argument converts this pointwise domination into the convex approximation property in every source dimension. We also show that the Oka property extends across proper closed complex analytic subsets: if $A$ is such a subset of a connected complex manifold $X$ and $X\setminus A$ is Oka, then $X$ is Oka. The criterion has broad applications and produces many new examples of Oka manifolds.
发表机构
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
- University of Chinese Academy of Sciences（中国科学院大学）
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