Details:
Title  Minimal fields of definition for simplicial arrangements in the real projective plane.  Author(s)  Michael Cuntz  Type  Article in Journal  Abstract  For each simplicial arrangement in the real projective plane of the catalogue of B. Grünbaum [Ars Math. Contemp. 2, No. 1, 1–25 (2009; Zbl 1177.51020)], 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  simplical arrangement; oriented matroid; field of definition  ISSN  17816475 
Language  English  Journal  Innov. Incidence Geom.  Volume  12  Pages  4960  Publisher  Academia Press, Gent  Year  2011  Edition  0  Translation 
No  Refereed 
No 
