Reducibility And Factorization Of Central Hyperplane Arrangement

People have paid close attention to hyperplane arrangements and matroids in these thirty years in the world. In this thesis, matroid theory is used to study the reducibility and other related topics of central hyperplane arrangements.Along with the increasing dimension of the ambient space and the number of hyperplanes, the arrangements will become more and more complicated. In order to understand various arrangements, analyze their properties and characteristics, we hope to decompose the arrangements into several basic atoms, so that the study can be easier. Concretely, we hope to know whether a central hyperplane arrangement can be decomposed into several irreducible subarrangements or not. Thus, we can transfer the study of complicated arrangements into their irreducible subarrangements.A central non-essential arrangement can always be decomposed into the product of an empty arrangement and a central essential arrangement.