Reducibility of hyperplane arrangements

被引：0
作者：
Guang-feng Jiang
Jian-ming Yu
机构：
[1] Beijing University of Chemical Technology,Department of Mathematics
[2] Chinese Academy of Sciences,Academy of Mathematics and Systems Science
来源：
Science in China Series A: Mathematics | 2007年 / 50卷
关键词：
hyperplane arrangement; irreducible component; logarithmic derivation; 32S22; 14N20;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：689 / 697
页数：8
相关论文
共 31 条
[1]  
Cordovil R.(1994)On the center of the fundamental group of the complement of a hyperplane arrangement Portugaliae Mathematica 51 363-373
[2]  
Cohen D.(1995)On Milnor fibrations of arrangements J Lodon Math Soc 51 105-119
[3]  
Suciu A.(2002)Some cyclic covers of complements of arrangements Topology & Appl 118 3-15
[4]  
Cohen D.(2003)Gauss-Manin connections for arrangements, I. Eigenvalues Compositio Math 136 299-316
[5]  
Orlik P.(2005)Gauss-Manin connections for arrangements, II. Nonresonant weights Amer J Math 127 569-594
[6]  
Cohen D.(2005)Gauss-Manin connections for arrangements, III. Formal connections Trans Amer Math Soc 357 3031-3050
[7]  
Orlik P.(2006)Gauss-Manin connections for arrangements, IV. Nonresonant eigenvalus Comment Math Helv 81 883-909
[8]  
Cohen D.(1991)Arrangements of hyperplanes and Lie algebra homology Invent Math 106 139-194
[9]  
Orlik P.(1992)Cohomology of local systems of the complement of hyperplanes Invent Math 109 557-561
[10]  
Cohen D.(1995)Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors J Pure and App Alg 100 93-102
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