zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Matroid polytopes, nested sets and Bergman fans. (English) Zbl 1092.52006
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.

52B20Lattice polytopes (convex geometry)
05B35Matroids, geometric lattices (combinatorics)
14D99Families, fibrations
52B40Matroids (convex geometry)
52C35Arrangements of points, flats, hyperplanes
Full Text: EuDML arXiv