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arXiv · 1201.5010

Line arrangements modeling curves of high degree: equations, syzygies and secants

Gregory Burnham·Zvi Rosen·Jessica Sidman·Peter Vermeire
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Abstract

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.

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Gregory Burnham, Zvi Rosen, Jessica Sidman, Peter Vermeire. 2015-05-15. Line arrangements modeling curves of high degree: equations, syzygies and secants. https://arxiv.org/abs/1201.5010

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