40 citations · 221 across the 19 of their papers we have counts for
7 papers · 1 filter
Geometric Equations for Matroid Varieties
Jessica Sidman, Will Traves, Ashley Wheeler
Each point in Gr corresponds to an matrix which gives rise to a matroid on its columns. Gel'fand, Goresky, MacPherson, and Serganova showed that…
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…
Linear determinantal equations for all projective schemes
Jessica Sidman, Gregory G. Smith
We prove that every projective embedding of a connected scheme determined by the complete linear series of a sufficiently ample line bundle is defined by the 2-minors of a 1-generi…
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…
Syzygies of the secant variety of a curve
Jessica Sidman, Peter Vermeire
We show that the secant variety of a linearly normal smooth curve of degree at least 2g+3 is arithmetically Cohen-Macaulay, and we use this information to study the graded Betti nu…
Secant varieties of toric varieties
David Cox, Jessica Sidman
Let be a smooth projective toric variety of dimension embedded in $\PP^r$ using all of the lattice points of the polytope . We compute the dimension and degree of the…