%0 Journal Article
%T Gr£¿bner bases of syzygies and Stanley depth
%A Gunnar Floystad
%A Juergen Herzog
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.jalgebra.2010.10.032
%X 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.
%U http://arxiv.org/abs/1003.4495v1