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 language||English (US)|
|Title of host publication||Configuration Spaces|
|Subtitle of host publication||Geometry, Combinatorics and Topology|
|Publisher||Scuola Normale Superiore|
|Number of pages||18|
|State||Published - Jan 1 2012|
ASJC Scopus subject areas