%0 Journal Article
%T Line arrangements modeling curves of high degree: equations, syzygies and secants
%A Gregory Burnham
%A Zvi Rosen
%A Jessica Sidman
%A Peter Vermeire
%J Mathematics
%D 2012
%I arXiv
%X We study curves consisting of unions of projective lines whose intersections are given by graphs. Under suitable hypotheses on the graph, these so-called \emph{graph curves} can be embedded in projective space as line arrangements. We discuss property $N_p$ for these embeddings and are able to produce products of linear forms that generate the ideal in certain cases. We also briefly discuss questions regarding the higher-dimensional subspace arrangements obtained by taking the secant varieties of graph curves.
%U http://arxiv.org/abs/1201.5010v2