Topological Study on the Degeneration Phenomena of Riemann Surfaces

在本课题的研究过程中，我们在将一根复杂的奇异光纤分裂成若干根简单的奇异光纤的问题上取得了很好的进展。除其他外，我们想指出荒川和足利的证明分裂的超椭圆奇异纤维和高村的研究建设分裂家庭不一定超椭圆奇异纤维，高村是一个合作的研究人员。实验方法对研究奇异纤维的劈裂也是非常重要的。事实上，Ahara开发了一个软件“Spritica”，通过该软件，我们可以在计算机显示器上观察“星形”奇异纤维的分裂运动。关于单值性的整体研究，Imayoshi、Ito和Yamamoto从函数论的角度进行了研究。此外，困境的绳索这可能是重要的研究莱夫谢茨纤维化，Kamada和松本研究了他们的代数表示。得到了许多其他相关的结果。

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.