Linear determinantal equations for all projective schemes (2009)
Sidman, Jessica, Smith, Gregory G.
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-generic matrix of linear...
Equations defining secant varieties: geometry and computation (2009)
Sidman, Jessica, Vermeire, Peter
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. Similar results hold...
Syzygies of the secant variety of a curve (2008)
Sidman, Jessica, Vermeire, Peter
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 numbers of the secant...
Defining Equations of Subspace Arrangements Embedded in Reflection Arrangements (2008)
Let k be an arbitrary field. An arrangement A of linear subspaces is a finite union of (possibly affine) linear subspaces in kn, among which there are no nontrivial containments. If all of the...
Jessica Sidman, Clare Boothe, Luce Program, Jessica Sidman, Mount Holyoke, College Intersection, ...
defined at p.
Prolongations and computational algebra (2006)
Sidman, Jessica, Sullivant, Seth
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 secant varieties. We...
Multigraded regularity: coarsenings and resolutions (2005)
Sidman, Jessica, Van Tuyl, Adam, Wang, Haohao
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 find finite...
Secant varieties of toric varieties (2005)
Let $X_P$ be a smooth projective toric variety of dimension $n$ embedded in $\PP^r$ using all of the lattice points of the polytope $P$. We compute the dimension and degree of the secant variety...
Subspace arrangements defined by products of linear forms (2005)
Anders Björner, Irena Peeva, Jessica Sidman
Abstract. We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a...
Subspace arrangements defined by products of linear forms (2005)
Anders Björner, Irena Peeva, Jessica Sidman
Abstract. We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a...
Multigraded regularity: syzygies and fat points (2004)
Sidman, Jessica, Van Tuyl, Adam
The Castelnuovo-Mumford regularity of a graded ring is an important invariant in computational commutative algebra, and there is increasing interest in multigraded generalizations. We study...
Generic initial ideals of points and curves (2004)
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 by Mark Green to...
Subspace arrangements defined by products of linear forms (2004)
Björner, Anders, Peeva, Irena, Sidman, Jessica
We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial...
Defining equations of subspace arrangements embedded in reflection arrangements (2004)
We give explicit generators for ideals of two classes of subspace arrangements embedded in certain reflection arrangements, generalizing results of S.-Y. R. Li and W. C. W. Li, and Kleitman and...
Defining equations of subspace arrangements embedded in reflection arrangements (2003)
We give explicit generators for ideals of two classes of subspace arrangements embedded in certain reflection arrangements, generalizing results of Li-Li and Kleitman-Lovasz. We also give minimal...
Castelnuovo-Mumford regularity by approximation (2002)
Derksen, Harm, Sidman, Jessica
The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given a system of approximating modules whose regularities are known. Such...
On the Castelnuovo-Mumford regularity of products of ideal sheaves (2001)
In this paper we give bounds on the Castelnuovo-Mumford regularity of products of ideals and ideal sheaves. In particular, we show that the regularity of a product of ideals is bounded by the sum of...
A sharp bound for the Castelnuovo-Mumford regularity of subspace arrangements (2001)
Derksen, Harm, Sidman, Jessica
We show that the ideal of an arrangement of d linear subspaces of projective space is d-regular in the sense of Castelnuovo and Mumford, answering a question of B. Sturmfels. In particular this...