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Research on Complex Analytic Properties of Complex Homogeneous Spaces

复齐次空间的复解析性质研究

基本信息

批准号：
09640174
负责人：
TAKEUCHI Shigeru
金额：
$ 1.73万
依托单位：
Gifu 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 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640174/
关键词：
CR VECTOR SPACE CR HERIMITIAN METRIC DR VECTOR SPACE CR TENSOR PRODUCT ADDITIVE CATEDORY POLARIZATION CR双対空間外積代数

项目摘要

One of the main objectives of this research project is to find necessary and sufficient conditions for homogeneous spaces of Lie groups to have a (bi-)invariant CR structure. Then next we have the task to classify them complex analytically. During the term of the project we obtained some of the basic properties of the category of CR vector spaces. We could apply them to investigate the conditions mentioned above and then to pursue the classification. These tasks are, however, not yet accomplished at the present moment, but are left for the future study We now list up some of the remarkable results of each investigator.(1) Takeuchi's result : He gave a new notion of CR tensor product of CR vector spaces, which generalizes that of the tensor product in the category of modules.(2) Hatada studied relations, on structure, among spaces of modular forms in positive characteristics and theirsubspaces. He studied also methods for explicit computations of the traces of Hecke operators with respect to spaces of complex modular forms and their invariant subspaces, and applications of them.(3) Fujimoto's result : (i) A rational elliptic surface with many torsion sections is, by a birational transformation, transformed to a rational elliptic surface with a multiple fiber. (ii) A non-singular projective threefold with a non-negative Kodaira dimension admitting an (nonisomorphic) onto self-holomorphism, has a non-singular minimal model and if the Kodaira dimension=2, or 0, it has a finite etale covering isomorphic to an Abelian threefold, or a direct product of a smooth surface and an elliptic curve.

这个研究项目的主要目标之一是找到李群的齐性空间具有（双）不变CR结构的充分必要条件。接下来，我们的任务是对它们进行复杂的分析分类。在项目期间，我们得到了CR向量空间范畴的一些基本性质。我们可以应用它们来研究上述情况，然后进行分类。然而，这些任务目前还没有完成，而是留给未来的研究，我们现在列出每个研究者的一些显着成果。(1)Takeuchi的结果：他给出了CR向量空间的CR张量积的新概念，推广了模范畴中张量积的概念。(2)Hatada研究了正特征模形式空间及其子空间之间的结构关系。他还研究了方法明确计算的痕迹Hecke运营商相对于空间的复杂的模块化形式及其不变的子空间，并应用它们。(3)Fujimoto的结果：（i）通过双有理变换，将一个具有多个挠截面的有理椭圆曲面变换为一个具有重纤维的有理椭圆曲面。(ii)具有非负科代拉维数的非奇异射影三重映射允许一个（非同构的）到自全纯上，具有非奇异极小模型，并且如果科代拉维数=2或0，则它具有同构于阿贝尔三重映射的有限代数覆盖，或光滑曲面与椭圆曲线的直积。