Study of the stability theory of polarized compact Kahler manifolds

极化紧致卡勒流形稳定性理论研究

基本信息

批准号：
02640046
负责人：
FUJIKI Akira
金额：
$ 1.15万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

项目摘要

We have obtained the following results concerning our research project.l. A. Fujiki : (1)has introduced a hyper kahler structure on the module space of representations of the fundamental group of a compact Kahler manifold and has studied, its properties, (2)has studied the existence and the uniquenss of extremal Kahler metrics on a ruled manifolds, (3)has shown an L Dolbeault lemma on a quasi-projective manifold and given its applications to deformations of locally symmetric varieties and to the existence of a Kahler-Einstein metric, and(4)has constructed a natural parabolic sheaf starting from a hermitian vector bundle with certain curvature growth condition defined on a quasi-projective manifold.2. M. Ue has determined the differentiable and geometric structures. together with the deformations of the latter on certain general 4-dimensional Sei Seifert fiber spaces and has also found some exotic differentiable structures, Where the study of elliptic surfaces is especially relevant.3. T. Ueda has studied the iterations of analytic transformations with parabolic fixed point set. Further, he has obtained a condition for a rational curve with a node in a complex surface to admit a strongly pseudoconcave neighborhood. 4. A. Gyouia has given general and explict methods of constructing relative invariants on a prehomogeneous vector space, computing their Fourier transforms and b-functions. Moreover, he has given a counter-example concerning the group action on such a vector space, and developped a representation of theory of group schems 5. H. Saito has given the classification and the product formula for the representations of quaternion algebras over local fields, with a trace formula for a certain Hecke operator as its application. He has also given the characters of the admissible representations of GL(2)via the theory of base change.

我们已经获得了有关我们的研究项目的以下结果。 A. Fujiki : (1)has introduced a hyper kahler structure on the module space of representations of the fundamental group of a compact Kahler manifold and has studied, its properties, (2)has studied the existence and the uniquenss of extremal Kahler metrics on a ruled manifolds, (3)has shown an L Dolbeault lemma on a quasi-projective manifold and given its applications to deformations局部对称品种和Kahler-Einstein度量的存在，（4）已从赫尔米尔人的载体束开始构建了自然的抛物线捆，具有在准标准歧管上定义的某些曲率生长条件。2。 M. UE确定了可区分和几何结构。连同后者在某些一般的4维SEI SEIFERT纤维空间上的变形，还发现了一些异国情调的结构，其中椭圆表面的研究特别相关。3。 T. UEDA研究了使用抛物线固定点集的分析转换的迭代。此外，他已经获得了一个在复杂表面的节点的理性曲线的条件，以接收一个强烈的伪有孔社区。 4。A.Gyouia给出了在固定媒介空间上构建相对不变的一般和解释方法，计算其傅立叶变换和B功能。此外，他为在这种矢量空间上的小组行动进行了反示例，并制定了组方案理论的表示。H。Saito给出了分类和乘积公式，用于在本地领域的五季度代数代表，并用特定的Hecke操作员将痕量公式作为其应用程序。他还通过基本变化理论给出了GL（2）的可接受表示的特征。