The contravariant form on singular vectors of a projective arrangement
Combinatorics
2011-08-22 v1
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 the sum of the weights a(H), H in A, is zero, then 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.
Keywords
Cite
@article{arxiv.1108.3871,
title = {The contravariant form on singular vectors of a projective arrangement},
author = {Michael J. Falk and Alexander N. Varchenko},
journal= {arXiv preprint arXiv:1108.3871},
year = {2011}
}
Comments
12 pages, no figures