Bergman Complexes and Coxeter Arrangements.
Combinatorial Aspects of Hyperplane Arrangements
November 01,2004 03:30 PM to 04:00 PM
Speakers:
Ardila, Federico
|
 |
Abstract: |
Motivated by the study of the amoeba of a complex algebraic variety, we
associate to each matroid M a polyhedral complex B(M), called the
"Bergman complex". The aim of the talk is to describe the combinatorics
and topology of this complex. B(M) is shown to be closely related to the
order complex of the lattice of flats of M; this shows that it is
homotopy equivalent to a wedge of spheres. If M is an oriented matroid,
the Bergman complex B(M) has a "positive part" associated to it, which
is also described.
The combinatorics is especially interesting for the matroid M_A of a
Coxeter arrangement A. The Bergman complex of M_A is equal to the nested
set complex of A, which arises in De Concini and Procesi's
compactification of the complement of A. The positive part of B(M_A) is
dual to the graph associahedron arising in the work of Carr and
Devadoss, Davis, and Postnikov.
|
Keywords: |
Hyperplane arrangements; amoeba; nested set complex. |
|
|
