Article ID Journal Published Year Pages File Type
4588943 Journal of Algebra 2006 25 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory