Discrete & Computational Geometry

, Volume 12, Issue 1, pp 49–63 | Cite as

Free arrangements and relation spaces

  • K. A. Brandt
  • H. Terao


Yuzvinsky [7] has shown that free arrangements are formal. In this note we define a more general class of arrangements which we callk-formal, and we show that free arrangements arek-formal. We close with an example which distinguishesk-formal arrangements from formal arrangements.


Exact Sequence Discrete Comput Geom Rank Function Relation Space Formal Arrangement 


  1. 1.
    M. Falk and R. Randell, On the homotopy theory of arrangements,Adv. Stud. Pure Math. 8 (1986), 101–124.MathSciNetGoogle Scholar
  2. 2.
    E. Kunz,Introduction to Commutative Algebra and Algebraic Geometry, Birkhäuser, Basel, 1985.MATHGoogle Scholar
  3. 3.
    P. Orlik and H. Terao,Arrangements of Hyperplanes, Grundlehren der Mathematischen Wissenschaften, Vol. 300, Springer-Verlag, Berlin, 1992.MATHGoogle Scholar
  4. 4.
    L. Solomon and H. Terao, A formula for the characteristic polynomial of an arrangement,Adv. in Math. 64 (1987) 305–325.MathSciNetCrossRefGoogle Scholar
  5. 5.
    H. Terao, Generalized exponents of a free arrangement of hyperplanes and Shephard-Todd-Brieskorn formula,Invent. Math. 63 (1981), 159–179.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    S. Yuzvinsky, Cohomology of local sheaves on arrangement lattices,Proc. Amer. Math. Soc. 112 (1991), 1207–1217.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    S. Yuzvinsky, First two obstructions to the freeness of arrangements,Trans. Amer. Math. Soc. 335 (1993), 231–244.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • K. A. Brandt
    • 1
  • H. Terao
    • 2
  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA
  2. 2.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations