Reducibility of hyperplane arrangements  

作　　者：Guang-feng JIANG & Jian-ming YU Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China 

出　　处：《Science China Mathematics》2007年第5期689-697,共9页中国科学：数学（英文版）

基　　金：the National Natural Science Foundation of China (Grant No. 10671009)

摘　　要：Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible components of a central hyperplane arrangement equals the dimension of the space consisting of the logarithmic derivations of the arrangement with degree zero or one. Secondly, it is proved that the decomposition of an arrangement into a direct sum of its irreducible components is unique up to an isomorphism of the ambient space. Thirdly, an effective algorithm for determining the number of irreducible components and decomposing an arrangement into a direct sum of its irreducible components is offered. This algorithm can decide whether an arrangement is reducible, and if it is the case, what the defining equations of irreducible components are.Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible components of a central hyperplane arrangement equals the dimension of the space consisting of the logarithmic derivations of the arrangement with degree zero or one. Secondly, it is proved that the decomposition of an arrangement into a direct sum of its irreducible components is unique up to an isomorphism of the ambient space. Thirdly, an effective algorithm for determining the number of irreducible components and decomposing an arrangement into a direct sum of its irreducible components is offered. This algorithm can decide whether an arrangement is reducible, and if it is the case, what the defining equations of irreducible components are.

关 键 词：hyperplane arrangement irreducible component logarithmic derivation 32S22 14N20 

分 类 号：O187.1[理学—数学]