Research on geometry related to Weyl groups and root systems

点击翻译按钮获取中文摘要

The zero set of the discriminant of an irreducible real reflection group is known to be a Saito free divisor. In this research project, we construct and classify Saito free divisors in a 3-dimensional affine space. Moreover we clarify the relationship between such divisors and families of deformations of simple curve singularities. As a next stage, we succeeded to construct systems of uniformization equations with singularities along such divisors and classified them. We also obtained some results of the structures of them. We could generalize these results to the case of complex reflection groups of rank three.