Complex analysis on quasi-Abelian varieties

1.我们得到了拟阿贝尔簇的周期矩阵的所有标准形式。利用这些形式，我们得到了拟阿贝尔簇纤维化定理的一个简单证明。进一步地，我们得到了关于阿贝尔变元的经典Riemann条件的另一个不依赖于调和积分理论的证明.作者在2001年10月于广岛召开的第五届真实的与复分析国际研讨会上作了上述结果的报告。大学）。他写的文件：拟阿贝尔簇的周期矩阵，包括环群的de Rham上同调，拟阿贝尔簇的周期矩阵和纤维化定理。这将发表在日本数学杂志vol.29-1（2003）.3。从周期矩阵的定理出发，得到了非代数复环面上具有主丛结构的拟阿贝尔簇的存在性。进一步，我们可以构造出许多不具有非常数亚纯函数的环群的例子 ...更多信息 nctions在他们身上这是一个扩展的方法西格尔谁建造的例子复杂的环面没有非常数亚纯函数对他们。如果没有科学研究补助金带来的计算机和软件，我们就无法构建这些例子。因为我们需要大量的计算矩阵，包括多项式。4.作者于2002年3月在日本数学学会会议上作了关于周期矩阵理论的演讲。此外，他在第六届真实的和复分析国际研讨会（2002年12月，广岛大学）上发表了关于周期矩阵定理的演讲。通过这些结果，我们认为本研究的主要目的已经达到.如上所述，我们使用计算机作为研究数学的重要工具。我们所开发的计算机数学教学方法将适用于数学教育。作者在信息处理教育会议（2002年10月，东京大学）上作了关于数学教育计算机化的报告。我们认为这些方法也是通过研究获得的。少

1. We obtained all standard forms of period matrices for quasi-Abelian varieties. Using these forms, we got a brief proof of fibration theorems for quasi-Abelian varieties. Further, we have an another proof, which does not depend on the theory of harmonic integrals, of classical Riemann conditions for Abelian varieties.2. The author gave a talk about the above results at the Fifth International Workshop on Real and Complex Analysis (October 2001, Hiroshima. University). He wrote the paper : Period matrices for quasi-Abelian Varieties, which includes de Rham cohomology of toroidal groups, period matrices and fibration theorems for quasi-Abelian varieties. This will be published in Japanese Journal of Mathematics vol.29-1(2003).3. From the theorems of period matrices, we found the existence of quasi-Abelian varieties which have principal bundle structures over non-algebraic complex tori. Further we could construct many examples of toroidal groups which have no non-constant meromorphic fu … More nctions on them. This is an extension of a method of Siegel who constructed examples of complex tori which have no non-constant meromorphic functions on them. We could not construct these examples without the computers and the softwares which was brought by the Grant-in-Aid for Scientic Research. Because we needed an enormous amount of calculations of matrices including polynomials.4. The author gave an lecture about the theory of period matrices as an invited talk at the conference of the mathematical society of Japan, March 2002. Further, he gave a talk about these examples obtained by the theorems of period matrices at the Sixth International Workshop on Real and Complex Analysis (December 2002, Hiroshima University). By these results, We think that the main aims of the research was obtained.5. As above, we use computers as important tools for a study of mathematics. The method of using computers for mathematics which we have developed will be applicable for mathematical educations. The author gave a talk about a computerization of mathematical education at the conference of information processing education (October 2002, Tokyo University). We think these methods were also obtained by the research. Less