Vol. 12, No. 1, 2011

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Minimal fields of definition for simplicial arrangements in the real projective plane

Michael Cuntz

Vol. 12 (2011), No. 1, 49–60
Abstract

For each simplicial arrangement in the real projective plane of the catalogue of Grünbaum, we determine the minimal extension of the rationals over which there exists a realization of its incidence structure. For the infinite families we use the symmetries of the incidence. For the sporadic arrangements we give an algorithm that uses Gröbner bases.

Keywords
simplicial arrangement, oriented matroid, field of definition
Milestones
Received: 4 May 2010
Accepted: 26 November 2010
Authors
Michael Cuntz
Department of Mathematics
University of Kaiserslautern
P.O. Box 3049
67653 Kaiserslautern
Germany