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arXiv · 1507.07706

Homological invariants of the Stanley-Reisner ring of a $k$-decomposable simplicial complex

Somayeh Moradi
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Abstract

We study the regularity and the projective dimension of the Stanley-Reisner ring of a $k$-decomposable simplicial complex and explain these invariants with a recursive formula. To this aim, the graded Betti numbers of $k$-decomposable monomial ideals which is the dual concept for $k$-decomposable simplicial complexes are studied and an inductive formula for the Betti numbers is given. As a corollary, for a chordal clutter $\mathcal{H}$, an upper bound for $reg(I(\mathcal{H}))$ is given in terms of the regularities of edge ideals of some chordal clutters which are minors of $\mathcal{H}$.

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Somayeh Moradi. 2015-07-28. Homological invariants of the Stanley-Reisner ring of a $k$-decomposable simplicial complex. https://arxiv.org/abs/1507.07706

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