Algebraic structures and complex structures of Quasi-Abelian varieties

1.利用周期矩阵的标准形式，证明了任何类型为Q型的n维拟阿贝尔丛都是q维阿贝尔簇上的C^&lt；*n-q&gt；-主丛。证明见于《拟阿贝尔变种的周期矩阵》，九州产业大学工学院公报，第36期(1999年)，第283-286.2页。进一步地，我们证明了对于每一个Q型拟阿贝尔簇C^n/Γ和类S，都存在相应的Q型和种类0的拟阿贝尔簇C^n/Γ满足以下条件：(1)C^n/Γ是C^n/Γ_0的覆盖流形；(2)定义了C^n/Γ上拟阿贝尔结构的充分黎曼型是由C^n/Γ_0诱导的。将此结果与文献1的结果相结合，得到了A.Andreotti-F.Gherardelli和Y.Abe3得到的拟阿贝尔簇的纤维定理。上述结果是在第三届实与复分析国际讲习班(6月，韩国梨花女子大学)、日本数学学会秋季会议(9月，京都大学)和第四届实与复分析国际讲习班(10月，广岛大学)上宣布的。包括这些结果的论文发表在《第三届实和复数分析国际研讨会论文集》(2000年)，第75-82期和《第四届实和复分析国际研讨会论文集》(2000年)，第81-87.4号。由2的结果，我们可以由类0的伴随拟阿贝尔簇构造出每一个拟阿贝尔簇。我们有许多这样的例子，这些例子将在稍后出版，使用的是科学研究补助金带来的计算机和软件。

1. We proved that any n-dimensional Quasi-Abelian variety of type q and kind 0 is a C^<*n-q>-principal bundle over an Abelian variety of dimension q, using our standard form of the period matrix. The proof is found in the paper : Period Matrices of Quasi-Abelian Varieties, Bulletin of the Faculty of Engineering, Kyushu Sangyo University 36(1999), 283-286.2. Further we showed that for every Quasi-Abelian variety C^n/Γ of type q and kind s, there exists an associated Quasi-Abelian variety C^n/Γ of type q and kind 0 satisfying the following conditions :(1) C^n/Γ is a covering manifold of C^n/Γ_0 and(2) The ample Riemann form which defines a Quasi-Abelian structure on C^n/Γ is induced by C^n/Γ_0. Combining this and the result of 1, we get the fibration theorems of Quasi-Abelian varieties which was obtained by A.Andreotti-F.Gherardelli and Y.Abe.3. The above results were announced in the Third International Workshop on Real and Complex Analysis (June, Ewha Womans University, Korea), Autumn Conference of Mathematical Society of Japan (September, Kyoto University) and the Fourth International Workshop on Real and Complex Analysis (October, Hiroshima University). Papers including these results were published in the Proceedings of the Third International Workshop on Real and Complex Analysis (2000), 75-82 and the Proceedings of the Fourth International Workshop on Real and Complex Analysis (2000), 81-87 .4. From the result of 2, we can construct every Quasi-Abelian variety from the associated Quasi-Abelian variety of kind 0. We have many examples of them which will be published later, using the computers and the softwares which was brought by the Grant-in-Aid for Scientic Research.