Topological Study on the Degeneration Phenomena of Riemann Surfaces

在项目期间，我们在将给定的复杂奇异纤维分裂成若干更简单的奇异纤维的问题上取得了相当好的进展。其中，我们想指出Arakawa和Ashikaga对超椭圆奇异纤维的可分性的证明，以及Takamura对不一定是超椭圆奇异纤维的分离族的构造的研究，Takamura是合作研究者。实验方法对于研究奇异纤维的分裂也是非常重要的。事实上，Ahara开发了一种软件“Splitica”，通过它，我们可以在计算机显示器上观察到“星形”奇异纤维的分裂运动。对于单元性的全球研究，Imayoshi、Ito、Yamamoto等人从函数理论的角度进行了研究。对于研究Lefschetz纤颤可能很重要的弦的困惑，Kamada和MatSumoto研究了它们的代数表示。还得到了许多其他相关结果。

During the term of the project, we have made quite a good progress on the problem of splitting a given complicated singular fiber into a number of simpler singular fibers. Among others, we would like to point out Arakawa and Ashikaga's proof of the splittability of hyperelliptic singular fibers and Takamura's research on the construction of splitting families for not necessarily hyperelliptic singular fibers, Takamura being a cooperative researcher. An experimental method is also very important to the study of splitting of singular fibers. In fact Ahara developed a software "Splitica" by which we can observe the splitting motion of "star-shaped" singular fibers on a computer display. As for the global study of monodromy, Imayoshi, Ito, and Yamamoto made a research from function theoretic viewpoint. Also the quandle of cords which might be important to the study of Lefschetz fibrations, Kamada and Matsumoto studied their algebraic representation. There are obtained many other related results.