乘积构形的超可解性

Reducibility of centered hyperplane arrangement

本文给出了乘积构形格的几个运算性质。证明了乘积构形格L中元素是模元的充要条件,并利用该结论证明了乘积构形(A1×…×Ak,V1…Vk)是超可解构形的充要条件是每个因子构形(Ai,Vi),1≤i≤k都是超可解构形。最后证明了若因子构形(Ai,Vi),1≤i≤k均是良分划构形,则乘积构形(A1×…×Ak,V1…Vk)也是良分划构形。

Sevaral operation characters in the lattice L of a product arrangement have been educed.It is proven that a product arrangement （A1×…×Ak,V1＋…＋Vk） is a supersolvable arrangement if, and only if,each arrangement Ai,Vi）,1≤i≤k is also a supersolvable arrangement.It is also proven that if each arrangement （Ai,Vi）,1≤i≤k is a nice patition, then the product arrangement （A1×…×Ak,V1＋…＋Vk） is alsoa nice patition.