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-Catalan构形的锥构形，构造其导子模的基底。(2) 对于超可解构形，研究使其成为归纳构形的超平面的次序问题，并研究此类超平面序的性质或特征。(3) 对于图构形，研究其Orlik-Solomon代数，并计算上同调代数及相关的拓扑不变量。

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 the basis for the derivation module of the cone over Shi-Catalan arrangement.(2)Studying the orders of hyperplanes which make a supersolvable arrangment be an inductively free arrangement, and giving the properties or characteristics for this kind of orders. (3)For graphical arrangements, doing research on the Orlik-Solomon algebras, and calculating the cohomology of the Orlik-Solomon algebras and related topological invariants.