# First Nonlinear Syzygies of Ideals Associated to Graphs - Mathematics > Commutative Algebra

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Abstract: Consider an ideal $I\subset Kx 1, ., x n$, with $K$ an arbitrary field,generated by monomials of degree two. Assuming that $I$ does not have a linearresolution, 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 theresolution nonlinear syzygies are concentrated in degree $s+3$, and we computethe corresponding graded Betti number $\beta {s,s+3}$. The multidegrees ofthese nonlinear syzygies are also determined and the corresponding multigradedBetti numbers are shown to be all equal to 1.

Autor: Oscar Fernandez-Ramos, Philippe Gimenez

Fuente: https://arxiv.org/