Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588943 | Journal of Algebra | 2006 | 25 Pages |
Abstract
Let S=k[x1,…,xn] be a Zr-graded ring with deg(xi)=ai∈Zr for each i and suppose that M is a finitely generated Zr-graded S-module. In this paper we describe how to find finite subsets of Zr containing the multidegrees of the minimal multigraded syzygies of M. To find such a set, we first coarsen the grading of M so that we can view M as a Z-graded S-module. We use a generalized notion of Castelnuovo–Mumford regularity, which was introduced by D. Maclagan and G. Smith, to associate to M a number which we call the regularity number of M. The minimal degrees of the multigraded minimal syzygies are bounded in terms of this invariant.
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