Discrete CATS Seminar
U N I V E R S I T Y
K E N T U C K Y
WHERE CATS =
845 PATTERSON OFFICE TOWER
"Supersolvable line arrangements: a computational approach"
University of Cincinnati
Monday, February 1, 2010
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.