Cohen–Macaulayness and computation of Newton graded toric rings

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• 作者：Mathias Schulze ; Uli Walther
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2009
• 出版时间：August 2009
• 年：2009
• 卷：213
• 期：8
• 页码：1522-1535
• 全文大小：996 K

文摘

Let be a positive semigroup generated by , and let be the associated semigroup ring over a field . We investigate heredity of the Cohen–Macaulay property from to both its -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 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.