Factorization of compact complex 3-folds which admit certain projective structures
Factorization of compact complex 3-folds which admit certain projective structures
复制标题
允许某些射影结构的紧凑复数三重因式分解
DOI：
10.2748/tmj/1178227770
复制
发表时间：
1989
影响因子：
0.5
通讯作者：
Masahide Kato
中科院分区：
文献类型：
--
作者：
Masahide Kato
一个复流形X，dim X= 3，是L类的，如果，根据定义，X包含一个子域，该子域是双全纯的到一个三维复射影空间中的射影线的邻域。在[Ka 2][Ka 3]中，我们定义了L类流形的复解析连通和（称为“连通运算”）。本文将考虑如何将L类紧流形分解为素流形。为了描述我们的结果，我们引入了L类流形的Klein组合，它是复解析连通和的推广。我们的第一个结果是，如果L类紧致流形是Schottky型的，那么它是Blanchard流形和L-Hopf流形的Klein组合（定理A）（定义见§ 1）。这个结果是一个类似的Kulkarni的[Ku]。我们将证明LHopf流形的一些性质（定理B，§4），并给出Blanchard流形的一个粗略分类（定理C，§ 5）。有许多肖特基型流形。事实上，我们看到Blanchard流形和L-Hopf流形的复解析连通和是Schottky型的（定理D）。我们的工作受到Kulkarni [Ku]的激励和强烈影响。定理A及其证明类似于他的定理6.3及其证明。我想向我的同事K表示衷心的感谢。Yokoyama为有益的讨论。
A complex manifold X, dim X= 3, is of Class L, if, by definition, X contains a subdomain which is biholomorphic to a neighborhood of a projective line in a complex projective space of dimension three. In [Ka2][Ka3], we have defined complex analytic connected sum (which was called "connecting operation") of manifolds of Class L. In this paper, we shall consider how to factorize a compact manifold of Class L into prime ones. To describe our results, we introduce Klein combination of manifolds of Class L, which is a generalization of complex analytic connected sum. Our first result is that, if a compact manifold of Class L is of Schottky type, then it is a Klein combination of Blanchard manifolds and L-Hopf manifolds (Theorem A) (see § 1 for the definitions). This result is an analogue of Kulkarni's [Ku]. We shall prove some properties of LHopf manifolds (Theorem B, §4) and give a rough classification of Blanchard manifolds (Theorem C, § 5). There are many manifolds of Schottky type. In fact, we see that a complex analytic connected sum of Blanchard manifolds and L-Hopf manifolds is of Schottky type (Theorem D). Our work is motivated and strongly influenced by that of Kulkarni [Ku]. Theorem A and its proof is an analogue of his Theorem 6.3 and its proof. I would like to express my hearty thanks to my colleague K. Yokoyama for the helpful discussions.