Castelnuovo–Mumford regularity of deficiency modules

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• 作者：Markus Brodmann ; Maryam Jahangiri ; Cao Huy Linh
• 关键词：Castelnuovo– ; Mumford regularity ; Deficiency modules
• 刊名：Journal of Algebra
• 出版年：2009
• 出版时间：15 October 2009
• 年：2009
• 卷：322
• 期：8
• 页码：2816-2838
• 全文大小：290 K

文摘

Let and let M be a finitely generated graded module of dimension d over a Noetherian homogeneous ring R with local Artinian base ring R₀. Let beg(M), gendeg(M) and reg(M) respectively denote the beginning, the generating degree and the Castelnuovo–Mumford regularity of M. If and nZ, let denote the R₀-length of the n-th graded component of the i-th R₊-transform module of M and let Kⁱ(M) denote the i-th deficiency module of M.

Our main result says, that reg(Kⁱ(M)) is bounded in terms of beg(M) and the “diagonal values” with j=0,…,d−1. As an application of this we get a number of further bounding results for reg(Kⁱ(M)).