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 ∑H∊A 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.
Partially supported by NSF grant DMS-1101508
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© 2012 Scuola Normale Superiore Pisa
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Falk, M.J., Varchenko, A.N. (2012). The contravariant form on singular vectors of a projective arrangement. In: Bjorner, A., Cohen, F., De Concini, C., Procesi, C., Salvetti, M. (eds) Configuration Spaces. CRM Series. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-431-1_11
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DOI: https://doi.org/10.1007/978-88-7642-431-1_11
Publisher Name: Edizioni della Normale, Pisa
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