%0 Journal Article
%T First Nonlinear Syzygies of Ideals Associated to Graphs
%A Oscar Fernandez-Ramos
%A Philippe Gimenez
%J Mathematics
%D 2008
%I arXiv
%X Consider an ideal $I\subset K[x_1,..., x_n]$, with $K$ an arbitrary field, generated by monomials of degree two. Assuming that $I$ does not have a linear resolution, we determine the step $s$ of the minimal graded free resolution of $I$ where nonlinear syzygies first appear, we show that at this step of the resolution nonlinear syzygies are concentrated in degree $s+3$, and we compute the corresponding graded Betti number $\beta_{s,s+3}$. The multidegrees of these nonlinear syzygies are also determined and the corresponding multigraded Betti numbers are shown to be all equal to 1.
%U http://arxiv.org/abs/0811.1865v1