The contravariant form on singular vectors of a projective arrangement

Michael J Falk, Alexander N. Varchenko

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

We define the flag space and space of singular vectors for an arrangement A of hyperplanes in projective space equipped with a system of weights a: A → ℂ. We show that the contravariant bilinear form of the corresponding weighted central arrangement induces a well-defined form on the space of singular vectors of the projectivization. If ΣHεA a(H) = 0, this form is naturally isomorphic to the restriction to the space of singular vectors of the contravariant form of any affine arrangement obtained from A by dehomogenizing with respect to one of its hyperplanes.

Original languageEnglish (US)
Title of host publicationConfiguration Spaces
Subtitle of host publicationGeometry, Combinatorics and Topology
PublisherScuola Normale Superiore
Pages255-272
Number of pages18
ISBN (Electronic)9788876424311
ISBN (Print)9788876424304
StatePublished - Jan 1 2012

Fingerprint

Singular Vectors
Arrangement
Hyperplane
Bilinear form
Projective Space
Well-defined
Isomorphic
Restriction
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Falk, M. J., & Varchenko, A. N. (2012). The contravariant form on singular vectors of a projective arrangement. In Configuration Spaces: Geometry, Combinatorics and Topology (pp. 255-272). Scuola Normale Superiore.

The contravariant form on singular vectors of a projective arrangement. / Falk, Michael J; Varchenko, Alexander N.

Configuration Spaces: Geometry, Combinatorics and Topology. Scuola Normale Superiore, 2012. p. 255-272.

Research output: Chapter in Book/Report/Conference proceedingChapter

Falk, MJ & Varchenko, AN 2012, The contravariant form on singular vectors of a projective arrangement. in Configuration Spaces: Geometry, Combinatorics and Topology. Scuola Normale Superiore, pp. 255-272.
Falk MJ, Varchenko AN. The contravariant form on singular vectors of a projective arrangement. In Configuration Spaces: Geometry, Combinatorics and Topology. Scuola Normale Superiore. 2012. p. 255-272
Falk, Michael J ; Varchenko, Alexander N. / The contravariant form on singular vectors of a projective arrangement. Configuration Spaces: Geometry, Combinatorics and Topology. Scuola Normale Superiore, 2012. pp. 255-272
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