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arXiv · 0912.2152

On the structure of Stanley-Reisner rings associated to cyclic polytopes

Janko Boehm·Stavros Argyrios Papadakis
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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.

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Janko Boehm, Stavros Argyrios Papadakis. 2011-10-24. On the structure of Stanley-Reisner rings associated to cyclic polytopes. https://arxiv.org/abs/0912.2152

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