1 citations · 5 across the 6 of their papers we have counts for
9 papers
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…
Splittable ideals and the resolutions of monomial ideals
Huy Tai Ha, Adam Van Tuyl
We provide a new combinatorial approach to study the minimal free resolutions of edge ideals, that is, quadratic square-free monomial ideals. With this method we can recover most o…
On the linear strand of an edge ideal
Mike Roth, Adam Van Tuyl
Let I(G) be the edge ideal associated to a simple graph G. We study the graded Betti numbers that appear in the linear strand of the minimal free resolution of I(G).
On the defining ideal of a set of points in multi-projective space
Adam Van Tuyl
We investigate the defining ideal of a set of points X in multi-projective space with a special emphasis on the case that X is in generic position, that is, X has the maximal Hilbe…
Powers of complete intersections: graded Betti numbers and applications
Elena Guardo, Adam Van Tuyl
Let I = (F_1,...,F_r) be a homogeneous ideal of R = k[x_0,...,x_n] generated by a regular sequence of type (d_1,...,d_r). We give an elementary proof for an explicit description of…
The regularity of points in multi-projective spaces
Huy Tai Ha, Adam Van Tuyl
Let I = p_1^{m_1} \cap ... \cap p_s^{m_s} be the defining ideal of a scheme of fat points in P^{n_1} x ... x P^{n_k} with support in generic position. When all the m_i's are 1, we…