arxiv: 0912.2152 · v2 · pith:4UUALM7Snew · submitted 2009-12-11 · 🧮 math.AC · math.CO

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

Janko Boehm , Stavros Argyrios Papadakis This is my paper

classification 🧮 math.AC math.CO

keywords deltaringsstanley-reisnercyclicassociatedcomplexgradedpolytopes

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

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