The contravariant form on singular vectors of a projective arrangement

Michael J Falk; Alexander N. Varchenko

doi:10.1007/978-88-7642-431-1_11

The contravariant form on singular vectors of a projective arrangement

Michael J Falk, Alexander N. Varchenko

Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Scopus citations

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 Σ_HεA 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 language	English (US)
Title of host publication	Configuration Spaces
Subtitle of host publication	Geometry, Combinatorics and Topology
Publisher	Scuola Normale Superiore
Pages	255-272
Number of pages	18
ISBN (Electronic)	9788876424311
ISBN (Print)	9788876424304
DOIs	https://doi.org/10.1007/978-88-7642-431-1_11
State	Published - Jan 1 2012

ASJC Scopus subject areas

General Mathematics

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The contravariant form on singular vectors of a projective arrangement

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