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

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

2012-01-24

arxiv.org/abs/1201.5010v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

We study curves consisting of unions of projective lines whose intersections are given by graphs. These so-called \emph{graph curves} can be embedded in projective space so their ideals are generated by products of linear forms. We discuss the minimal free resolution of the ideal of a graph curve and are able to produce products of linear forms that generate the ideal under certain hypotheses. We also study the higher-dimensional subspace arrangements obtained by taking the secant varieties of graph curves.

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