17 citations · 25 across the 14 of their papers we have counts for
15 papers
Betti Tables of Reducible Algebraic Curves
David J. Bruce, Pin-Hung Kao, Evan D. Nash +2
We study the Betti tables of reducible algebraic curves with a focus on connected line arrangements and provide a general formula for computing the quadratic strand of the Betti ta…
Line arrangements modeling curves of high degree: equations, syzygies and secants
Gregory Burnham, Zvi Rosen, Jessica Sidman +1
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…
Arithmetic properties of the first secant variety to a projective variety
Peter Vermeire
Under an explicit positivity condition, we show the first secant variety of a linearly normal smooth variety is projectively normal, give results on the regularity of the ideal of…
Equations and syzygies of the first secant variety to a smooth curve
Peter Vermeire
We show that if C is a linearly normal smooth curve embedded by a line bundle of degree at least 2g+3+p then the secant variety to the curve satisfies N_{3,p}.
Equations defining secant varieties: geometry and computation
Jessica Sidman, Peter Vermeire
In the 1980's, work of Green and Lazarsfeld helped to uncover the beautiful interplay between the geometry of the embedding of a curve and the syzygies of its defining equations. S…
Generation and syzygies of the first secant variety
Peter Vermeire
Under certain effective positivity conditions, we show that the secant variety to a smooth variety satisfies . For smooth curves, we provide the best possible effective bo…