On the structure of Stanley-Reisner rings associated to cyclic polytopes
Commutative Algebra
2012-07-19 v2 Combinatorics
Abstract
We study the structure of Stanley-Reisner rings associated to cyclic polytopes, using ideas from unprojection theory. Consider the boundary simplicial complex Delta(d,m) of the d-dimensional cyclic polytope with m vertices. We show how to express the Stanley-Reisner ring of Delta(d,m+1) in terms of the Stanley-Reisner rings of Delta(d,m) and Delta(d-2,m-1). As an application, we use the Kustin-Miller complex construction to identify the minimal graded free resolutions of these rings. In particular, we recover results of Schenzel, Terai and Hibi about their graded Betti numbers.
Keywords
Cite
@article{arxiv.0912.2152,
title = {On the structure of Stanley-Reisner rings associated to cyclic polytopes},
author = {Janko Boehm and Stavros Argyrios Papadakis},
journal= {arXiv preprint arXiv:0912.2152},
year = {2012}
}
Comments
Version 2, minor improvements, 20 pages. Package may be downloaded at http://www.math.uni-sb.de/ag/schreyer/jb/Macaulay2/CyclicPolytopeRes/html/