Extension property of holomorphic maps and the structure of complex manifolds

本文研究了一种通过度量Hartogs域上的全纯映射到给定复流形上的可扩性来获得复流形结构信息的方法。作为该方法的一个应用，我们得到了如下结果.对于一个具有不连续性条件的三维离散射影变换群Γ，我们可以定义一个射影空间的开子集的非奇异商空间X（Γ）.我们证明了，如果X（Γ）包含一个代数维数为正的紧连通分支，则X（Γ）是连通的，并且X（Γ）是双全纯的三种著名的3-折叠之一.

We are studying a method to get some information of the structure of a given complex manifold by measuring the extendibility of holomorphic maps of Hartogs domains to the given manifold. As an application of the method, we have obtained the following result. For a finitely generated three dimensional discrete projective transformation group Γ with some discontinuity condition, we can define canonically a non-singular quotient space X(Γ) of an open subset of a projective 3-space. We have shown that, if X(Γ) contains a compact connected component with positive algebraic dimension, then X(Γ) is connected, and that X(Γ) is biholomorphic to one of the three kinds of well-known 3-folds.