Cohen-Macaulayness and computation of Newton graded toric rings

Details Cohen-Macaulayness and computation of Newton graded toric rings Cohen-Macaulayness and computation of Newton graded toric rings

2007-06-25

arxiv.org/abs/0706.3545v1

J. Pure Appl. Alg. 213,8 (2009), 1522-1535.

Mathematics

Commutative Algebra

20 pages, 4 figures

Scientific paper

10.1016/j.jpaa.2008.11.035

Let $H$ be a positive semigroup in $\mathbb{Z}^d$ generated by $A$, and let $K[H]$ be the associated semigroup ring over a field $K$. We investigate heredity of the Cohen-Macaulay property from $K[H]$ to both its $A$-Newton graded ring and to its face rings. We show by example that neither one inherits in general the Cohen-Macaulay property. On the positive side we show that for every $H$ there exist generating sets $A$ for which the Newton graduation preserves Cohen-Macaulayness. This gives an elementary proof for an important vanishing result on $A$-hypergeometric Euler-Koszul homology. As a tool for our investigations we develop an algorithm to compute algorithmically the Newton filtration on a toric ring.

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