Research on geometry related to Weyl groups and root systems

已知不可约真实的反射群的判别式的零集是Saito自由因子。在本研究计画中，我们在三维仿射空间中构造并分类Saito自由因子。此外，我们阐明了这类因子与简单曲线奇异变形族之间的关系。作为下一个阶段，我们成功地构建系统的均匀化方程的奇性沿着这样的因子和分类。我们还得到了它们的结构的一些结果。我们可以把这些结果推广到秩为3的复反射群的情形。

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.