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

G. Burnham; Z. Rosen; J. Sidman; P. Vermeire

doi:10.1007/9781107416000.005

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

G. Burnham, Z. Rosen, J. Sidman, P. Vermeire

COLLEGE OF SCIENCE & ENGINEERING

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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 graph curves can be embedded in projective space as line arrangements. We discuss property N_pfor 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.

Original language	English
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
Pages	52-70
Number of pages	19
ISBN (Electronic)	9781107416000
ISBN (Print)	9781107647558
DOIs	https://doi.org/10.1007/9781107416000.005
State	Published - Jan 1 2015

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10.1007/9781107416000.005

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

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