We study curves consisting of unions of projective lines whose intersections are given by graphs. Under suitable hypotheses on the graph, these so-called graph curves can be embedded in projective space as line arrangements. We discuss property Npfor these embeddings and are able to obtain 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.
|Title of host publication||Recent Advances in Algebraic Geometry|
|Subtitle of host publication||A Volume in Honor of Rob Lazarsfeld's 60th Birthday|
|Publisher||Cambridge University Press|
|Number of pages||19|
|State||Published - Jan 1 2015|