Study on Saito free divisors and uniformization equations

主要研究了仿射三维空间中的Saito自由因子。众所周知，任何不可约复反射群的判别式的零集都是Saito自由因子。在秩3的情况下，我们沿着判别式的零集完成了齐次化微分方程组的分类。研究结果发表在《九州数学杂志》上。在具有简单奇点的单参数曲线族构成的仿射三维空间中，有17个Saito自由因子。我们完成了沿着这样的Saito自由因子具有奇异性的2阶完整系统的分类。

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.