### 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) |
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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 |

State | Published - Jan 1 2012 |

### ASJC Scopus subject areas

- Mathematics(all)

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## 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.