仿射构形的可约性

The reducibility of affine hyperplane arrangements

用矩阵方法讨论仿射超平面构形的可约性。通过证明仿射构形可约等价于对应的中心构形可约,把仿射构形因子分解存在惟一性归结为中心构形相应的已知结论,得到仿射超平面构形因子分解的存在惟一性。

The reducibility of affine hyperplane arrangements is discussed by using the matrix method. It is proved that an affine arrangement is reducible if, and only if, its corresponding central arrangement is reducible. Thus the existence and uniqueness of affine hyperplane arrangement decompositions is changed into that of the corresponding central hyperplane arrangement decompositions and, therefore, the existence and uniqueness of affine hyperplane arrangement decompositions is obtained.