Study on Saito free divisors and uniformization equations

主要研究了三维仿射空间中的Saito自由因子。已知任何不可约复反射群的判别式的零集是Saito自由因子。在秩为3的情况下，我们完成了微分方程一致化系统沿着判别式零集的分类。结果发表在《九州数学杂志》上。在由具有简单奇点的单参数曲线族构成的仿射三维空间中，存在17个Saito自由因子。我们完成了一个分类的秩2完整系统的奇性沿着这样的斋藤自由因子。

Mainly Saito free divisors in an affine 3-dimensional space are studied. It is known that the zero set of the discriminant of any irreducible complex reflection group is a Saito free divisor. In the rank 3 case, we accomplished a classification of uniformization systems of differential equations along the zero set of discriminant. The result is published in Kyushu J. Math. There are seventeen Saito free divisors in an affine 3 dimensional space constructed by 1-parameter families of curves with simple singularities. We accomplished a classification of holonomic systems of rank 2 with singularities along such Saito free divisors.