40 citations · 221 across the 19 of their papers we have counts for
8 papers · 1 filter
Linearizing Algebraic Matroids
Zvi Rosen, Jessica Sidman, Louis Theran
Although algebraic matroids were discovered in the 1930s, interest in them was largely dormant until their recent use in applications of algebraic geometry. Because nonlinear algeb…
Geometric aspects of the Jacobian of a hyperplane arrangement
Michael DiPasquale, Jessica Sidman, Will Traves
An embedding of the complete bipartite graph in gives rise to both a line arrangement and a bar-and-joint framework. For a generic placement of the six ver…
Prolongations and computational algebra
Jessica Sidman, Seth Sullivant
We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for sec…
Multigraded regularity: coarsenings and resolutions
Jessica Sidman, Adam Van Tuyl, Haohao Wang
Let S = k[x_1,...,x_n] be a Z^r-graded ring with deg (x_i) = a_i \in Z^r for each i and suppose that M is a finitely generated Z^r-graded S-module. In this paper we describe how to…
Multigraded regularity: syzygies and fat points
Jessica Sidman, Adam Van Tuyl
The Castelnuovo-Mumford regularity of a graded ring is an important invariant in computational commutative algebra, and there is increasing interest in multigraded generalizations.…
Generic initial ideals of points and curves
Aldo Conca, Jessica Sidman
Let I be the defining ideal of a smooth irreducible complete intersection space curve C with defining equations of degrees a and b. We use the partial elimination ideals introduced…