Abstract
We study the exactness of certain combinatorially defined complexes which generalize the Orlik-Solomon algebra of a geometric lattice. The main results pertain to complex reflection arrangements and their restrictions. In particular, we consider the corresponding relation complexes and give a simple proof of the n-formality of these hyperplane arrangements. As an application, we are able to bound the Castelnouvo-Mumford regularity of certain modules over polynomial rings associated to Coxeter arrangements (real reflection arrangements) and their restrictions. The modules in question are defined using the relation complex of the Coxeter arrangement and fiber polytopes of the dual Coxeter zonotope. They generalize the algebra of piecewise polynomial functions on the original arrangement.
Original language | English |
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Pages (from-to) | 901-947 |
Number of pages | 47 |
Journal | Israel Journal of Mathematics |
Volume | 201 |
Issue number | 2 |
DOIs | |
State | Published - 2 Oct 2014 |
All Science Journal Classification (ASJC) codes
- General Mathematics