Beiträge zur Algebra und Geometrie <BR> Contributions to Algebra and GeometryVol. 40, No. 2, pp. 283-289 (1999)

The Largest Intersection Lattice of a Discriminantal Arrangement

Christos A. Athanasiadis

Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA, email:

Abstract: We prove a conjecture of Bayer and Brandt [J. Alg. Combin. 6 (1997), 229-246] about the "largest" intersection lattice of a discriminantal arrangement based on an essential arrangement of $n$ linear hyperplanes in $\hbox R^k$. An important ingredient in the proof is Crapo's characterization of the matroid of circuits of the configuration of $n$ generic points in $ R^k$.

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