超平面构形是奇点理论的一个分支，它是一类具有非孤立奇点的超曲面。超平面构形是处在组合学、代数学、拓扑学、代数几何学等多个学科交汇处的一门年轻的学科，它的巨大魅力在于：能从组合学以及代数学等不同角度去描述它的拓扑不变量。我们主要研究：(1) 对于Shi构形的锥构形，构造出统一形式的导子模的基底公式。(2) 对于由若干超平面和以原点为球心的球面所形成的混杂构形，给出判断其自由性的充要条件。另外，对于自由混杂构形，构造其导子模的基底。

The arrangement of hyperplanes is a branch of singularity theory, it is a hypersurface with non-isolated singularities. We can study arrangements with methods from combinatorics, algebra, topology, algebraic geometry and so on. The greatest charm of the theory of hyperplane arrangements is expressing topological invariants of the complement space in terms of combinatorics or algebra. We will study on the following three subjects: (1) Giving an explict construction of a universal basis for the derivation module of the cone over Shi arrangement.(2) For the mixed arrangement, which consists of a hyperplane arrangement and several spheres centered at origin, giving a sufficient and necessary condition for the freeness of it, and constructing bases for the free mixed arrangements of that kind.