Research on geometry related to Weyl groups and root systems

已知不可约实反射群的判别式的零集是齐东自由约数。在本研究项目中，我们在三维仿射空间中构造并分类了Saito自由因子。此外，我们还阐明了这些除数与简单曲线奇异变形族之间的关系。下一步，我们成功地构造了具有奇异性的均匀化方程组，并对它们进行了分类。我们还得到了它们的一些结构结果。我们可以将这些结果推广到3阶复反射群的情况。

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.