Gröbner bases of syzygies and Stanley depth

Details Gröbner bases of syzygies and Stanley depth Gröbner bases of syzygies and Stanley depth

2010-03-23

arxiv.org/abs/1003.4495v1

Journal of Algebra 328 (2011), no.1, p.178-189

Mathematics

Commutative Algebra

13 pages

Scientific paper

10.1016/j.jalgebra.2010.10.032

Let F. be a any free resolution of a Z^n-graded submodule of a free module over the polynomial ring K[x_1, ..., x_n]. We show that for a suitable term order on F., the initial module of the p'th syzygy module Z_p is generated by terms m_ie_i where the m_i are monomials in K[x_{p+1}, ..., x_n]. Also for a large class of free resolutions F., encompassing Eliahou-Kervaire resolutions, we show that a Gr\"obner basis for Z_p is given by the boundaries of generators of F_p. We apply the above to give lower bounds for the Stanley depth of the syzygy modules Z_p, in particular showing it is at least p+1. We also show that if I is any squarefree ideal in K[x_1, ..., x_n], the Stanley depth of I is at least of order the square root of 2n.

Affiliated with

Also associated with

No associations

Rating

Gröbner bases of syzygies and Stanley depth does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Gröbner bases of syzygies and Stanley depth, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gröbner bases of syzygies and Stanley depth will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-212001