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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.

关于我们的研究项目，我们取得了以下结果。A.藤木：（1）在紧致Kahler流形的基本群表示的模空间上引入了超Kahler结构，并研究了它的性质;（2）研究了规则流形上极值Kahler度量的存在性和唯一性;（3）证明了一个关于拟-射影流形，并给出它在局部对称簇的变形和Kahler-Einstein度量的存在性中的应用，（4）从定义在拟射影流形上的具有一定曲率增长条件的埃尔米特向量丛出发，构造了一个自然抛物层. M.确定了可微结构和几何结构。以及后者在某些一般4维Sei Seifert纤维空间上的变形，还发现了一些奇异的可微结构，其中椭圆曲面的研究尤其相关。3. T.上田研究了抛物型不动点集上解析变换的迭代问题。此外，他还得到了一个条件，有理曲线的节点在一个复杂的表面承认一个强伪凹的邻域。4. A. Gyouia给出了构造准齐次向量空间上的相对不变量、计算它们的傅里叶变换和b函数的一般和显式方法。此外，他还给出了一个关于这种向量空间上的群作用的反例，并发展了群schems理论的一个表示。H. Saito给出了局部域上四元数代数表示的分类和乘积公式，并给出了Hecke算子的迹公式。他还利用基变理论给出了GL（2）的容许表示的特征。