Projective structures on compex manifolds

复流形上的射影结构

基本信息

批准号：
09640129
负责人：
KATO Masahide
金额：
$ 2.18万
依托单位：
Sophia University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640129/
关键词：
complex manifold projective structure Gauduchon metric Hartogs domain non-Kahler extension peoblem Weyl curvature teusor Chern forms Characteristic forms projective connections 正則写像 Gauduchonメトリック特異ファイバー正則拡張性

项目摘要

Our main object of study is a class of compact complex 3-manifolds which contain a subdomain U biholomorphic to a neighborhood of a projective line ill a complex projective 3-space. We call such a class of manifolds by Class L. Such manifolds do not admit projective structures in general, but very deeply related to complex manifolds which admit projective structures. To classify all Class L. manifolds, it seems very important to consider the existence problem of Cauduchon metric near a singular fibre of a 1-parameter family of surfaces, and we are now very near to the complete solution.To carry out our plan of classification of Class L manifolds, a series of theorems of S. Ivashkovich on the extension of meromorphic maps play important roles. On the other hand, our manifolds of Class L supply us with many interesting examples on extension problems of meromorphic maps. N. Okada (Sophia Univ. Graduate Course) constructed an example of Schottky type Class L manifolds, gave a holomorphic map of a Hartogs domain to the manifold whichl cannot he extended meromorphically across a fractal set, and estimated the Hausdorff dimension of the singular set. With Y. Kamozawa (NTT), we have obtained a explicit formula of characteristic forms on a holomorphic foliation which admits a holomorphic projective connection.

我们的主要研究对象是一类紧凑的复合体3个序列，其中包含一个子域U生物形态，以射影线生病的一个复杂的投射3空间。我们称之为L级的一类流形。这样的歧管通常不承认投射结构，而是与接纳投影结构的复杂流形密切相关。 To classify all Class L. manifolds, it seems very important to consider the existence problem of Cauduchon metric near a singular fibre of a 1-parameter family of surfaces, and we are now very near to the complete solution.To carry out our plan of classification of Class L manifolds, a series of theorems of S. Ivashkovich on the extension of meromorphic maps play important roles.另一方面，我们的L类歧管为我们提供了许多有趣的示例，内容涉及Meromormormormormormormorphic Maps的扩展问题。 N. okada（SophiaUniv。ArtineRouse课程）构建了Schottky Type类L歧管的示例，给了Hartogs域的全体形态图，并向歧管提供了他不能在分形集合上扩展Meromororormororormororormororormororormororormorormororormoror的图，并估计了单一奇数集的Hausdorff Dimension。借助Y. Kamozawa（NTT），我们在全体形态叶片上获得了一个明确的特征形式公式，该叶片接受了全体形态的投射连接。