Relation spaces of hyperplane arrangements and modules defined by graphs of fiber zonotopes

T Finis, Erez Lapid

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)901-947
Number of pages47
JournalIsrael Journal of Mathematics
Volume201
Issue number2
DOIs
StatePublished - 2 Oct 2014

All Science Journal Classification (ASJC) codes

  • General Mathematics

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