A note on discriminantal arrangements

Author:
Michael Falk

Journal:
Proc. Amer. Math. Soc. **122** (1994), 1221-1227

MSC:
Primary 52B30; Secondary 52B40

DOI:
https://doi.org/10.1090/S0002-9939-1994-1209098-1

MathSciNet review:
1209098

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a fixed affine arrangement of *n* hyperplanes in general position in . Let denote the set of general position arrangements whose elements are parallel translates of the hyperplanes of . Then is the complement of a central arrangement . 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 in terms of the original arrangement . In terms of the underlying matroids, realizes an adjoint of the dual of the matroid associated with . Using this description we show that, contrary to the conventional wisdom, neither the intersection lattice of nor the topology of is independent of the original arrangement .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1209098-1

Keywords:
Manin-Schechtman arrangement,
Grassmann stratum,
dual matroid,
adjoint

Article copyright:
© Copyright 1994
American Mathematical Society