Multigraded regularity: coarsenings and resolutions
Abstract
Let S = k[x_1,...,x_n] be a Z^rgraded ring with deg (x_i) = a_i \in Z^r for each i and suppose that M is a finitely generated Z^rgraded Smodule. In this paper we describe how to find finite subsets of Z^r 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 Zgraded Smodule. We use a generalized notion of CastelnuovoMumford 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 arXiv:
 arXiv:math/0505421
 Bibcode:
 2005math......5421S
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 13D02;
 13D45
 EPrint:
 20 pages, 1 figure