### Abstract

Let A_{0}be a fixed affine arrangement of n hyperplanes in general position in K^{k}. Let U(n, k) denote the set of general position arrangements whose elements are parallel translates of the hyperplanes of A_{0}. Then U(n, k) is the complement of a central arrangement B(n, k). These are the well-known discriminantal arrangements introduced by Y. I. Manin and V. V. Schechtman. In this note we give an explicit description of B(n, k) in terms of the original arrangement A_{0}. In terms of the underlying matroids, B(n, k) realizes an adjoint of the dual of the matroid associated with A_{0}. Using this description we show that, contrary to the conventional wisdom, neither the intersection lattice of B(n, k) nor the topology of U(n, k) is independent of the original arrangement A_{0}.

Original language | English (US) |
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Pages (from-to) | 1221-1227 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 122 |

Issue number | 4 |

DOIs | |

State | Published - 1994 |

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### Keywords

- Adjoint
- Dual matroid
- Grassmann stratum
- Manin-Schechtman arrangement

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics