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Zbl 1092.52006
Feichtner, Eva Maria; Sturmfels, Bernd
Matroid polytopes, nested sets and Bergman fans. (English)
[J] Port. Math. (N.S.) 62, No. 4, 437-468 (2005). ISSN 0032-5155; ISSN 1662-2758/e

This paper is concerned with the tropical variety defined by a system of linear equations with constant coefficients. It turns out, that this variety is the Bergman fan of an associated matroid. After discussing the relation between Bergman fan and nested set complexes of (arbitrary) lattices, the authors refine a result due to Ardila-Klivans in relation with triangulations of Bergman complexes. A relation of combinatorial results and algebraic geometry (in terms of complements of arrangements of hyperplanes in the complex space) is also described.
[J. L. Ramirez Alfonsin (Paris)]

MSC 2000:: *52B20 Lattice polytopes (convex geometry)
05B35 Matroids (combinatorics)
14D99 Families, fibrations
52B40 Matroids (convex geometry)
52C35 Arrangements of points, flats, hyperplanes

Cited in: Zbl 1127.05107

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