8 citations · 12 across the 8 of their papers we have counts for
5 papers · 1 filter
Sequentially Cohen-Macaulay Edge Ideals
Christopher A. Francisco, Adam Van Tuyl
Let G be a simple undirected graph on n vertices, and let I(G) \subseteq R = k[x_1,...,x_n] denote its associated edge ideal. We show that all chordal graphs G are sequentially Coh…
Some families of componentwise linear monomial ideals
Christopher A. Francisco, Adam Van Tuyl
Let R=k[x_1,...,x_n] be a polynomial ring over a field k. Let J={j_1,...,j_t} be a subset of [n]={1,...,n}, and let m_J denote the ideal (x_{j_1},...,x_{j_t}) of R. Given subsets J…
Grassmannians and representations
Dan Edidin, Christopher A. Francisco
In this note we use Bott-Borel-Weil theory to compute cohomology of interesting vector bundles on sequences of Grassmanians.
New approaches to bounding the multiplicity of an ideal
Christopher A. Francisco
We use the theory of resolutions for a given Hilbert function to investigate the multiplicity conjectures of Huneke and Srinivasan and Herzog and Srinivasan. To prove the conjectur…
On the componentwise linearity and the minimal free resolution of a tetrahedral curve
Christopher A. Francisco, Juan C. Migliore, Uwe Nagel
A tetrahedral curve is an unmixed, usually non-reduced, one-dimensional subscheme of projective 3-space whose homogeneous ideal is the intersection of powers of the ideals of the s…