"Supersolvable line arrangements: a computational approach"

Stefan Tohaneanu
University of Cincinnati

Monday, February 1, 2010
4:00 pm
845 POT

Abstract:

Because of their highly combinatorial content, supersolvable arrangements are the nicest class of hyperplane arrangements one can study from any point of view: topological, combinatorial or algebraic. In the first part of the talk I'll present a brief introduction to hyperplane arrangements: basic definitions, the Orlik-Solomon algebra, broken circuits, nbc-bases, etc.; and I'll present the Bjorner-Ziegler and Peeva criteria for the supersolvability of any hyperplane arrangement.

By line arrangements one understands a central, essential arrangement of hyperplanes in K^3 (K= field of characteristic 0). The advantage of working in this low dimension is that supersolvability has a visual/geometric interpretation that leads to a test of this property that does not require a nice ordering of the hyperplanes, like the two criteria mentioned above do. In the end we're going to see how coding theory can come in hand for effective implementation of the algorithm in Macaulay 2.