manuscripta mathematica

, Volume 71, Issue 1, pp 295–306

Complexified real arrangements of hyperplanes

  • William A. Arvola

DOI: 10.1007/BF02568407

Cite this article as:
Arvola, W.A. Manuscripta Math (1991) 71: 295. doi:10.1007/BF02568407


LetV be a finite dimensional vector space over the real or complex numbers. Areal (orcomplex)arrangementA inV is a finite collection of real (or complex) affine hyperplanes. A real arrangement inV can becomplexified to form a complex arrangement in the complex vector spaceA. The (complex)complement of a real arrangementA is defined byM(A)=V⊗ℂ−⋃HAH⊗ℂ. There are two different finite simplicial complexes which carry the homotopy type ofM(A), one given by M. Salvetti, the other by P. Orlik. In this paper we describe both complexes and exhibit a simplicial homotopy equivalence between them.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • William A. Arvola
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadison