Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A non-Hausdorff model for the complement of a complexified hyperplane arrangement

Author: Nicholas Proudfoot
Journal: Proc. Amer. Math. Soc. 135 (2007), 3989-3994
MSC (2000): Primary 52C35
Published electronically: September 12, 2007
MathSciNet review: 2341950
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given a hyperplane arrangement $ \mathcal{A}$ in a real vector space $ V$, we introduce a real algebraic prevariety $ \mathcal{Z}(\mathcal{A})$, and exhibit the complement of $ \mathcal{A}$ in the complexification of $ V$ as the total space of an affine bundle over $ \mathcal{Z}(\mathcal{A})$ with fibers modeled on the dual vector space $ V^{\vee}$.

References [Enhancements On Off] (What's this?)

  • [BD] R. Bielawski and A. Dancer.
    The geometry and topology of toric hyperkähler manifolds.
    Comm. Anal. Geom. 8 (2000), 727-760. MR 1792372 (2002c:53078)
  • [KN] G. Kempf and L. Ness.
    The length of vectors in representation spaces.
    Algebraic geometry (Proc. Summer Meeting, Univ. Copenhagen, Copenhagen, 1978), pp. 233-243,
    Lecture Notes in Math., 732, Springer, Berlin, 1979. MR 555701 (81i:14032)
  • [OS] P. Orlik and L. Solomon.
    Combinatorics and topology of complements of hyperplanes.
    Invent. Math. 56 (1980), 167-189. MR 558866 (81e:32015)
  • [PW] N. Proudfoot and B. Webster.
    Arithmetic and topology of hypertoric varieties.
    To appear in J. Alg. Geom.
  • [Sa] M. Salvetti.
    Topology of the complement of real hyperplanes in $ \C^N$.
    Invent. Math. 88 (1987), 603-618. MR 884802 (88k:32038)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 52C35

Retrieve articles in all journals with MSC (2000): 52C35

Additional Information

Nicholas Proudfoot
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027

Received by editor(s): July 15, 2006
Received by editor(s) in revised form: September 14, 2006
Published electronically: September 12, 2007
Additional Notes: This author was partially supported by an NSF Postdoctoral Research Fellowship
Communicated by: Ted Chinburg
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society