On the minimal free resolution of n + 1 general forms (2008)
Abstract. Let R = k[x1,...,xn] andletI be the ideal of n + 1 generically chosen forms of degrees d1 ≤···≤dn+1. We give the precise graded Betti numbers of R/I in the following cases: • n =3;...
Classifying Hilbert functions of fat point subschemes in $\mathbb P^2$ (2008)
Geramita, A. V., Harbourne, B., Migliore, J.
A recent paper by the first and third authors together with Sabourin raised the question of what the possible Hilbert functions are for fat point subschemes of the form $2p_1+...+2p_r$, for all...
A tetrahedral curve is a space curve whose defining ideal is an intersection of powers of monomial prime ideals of height two. It is supported on a tetrahedral configuration of lines. Schwartau...
On the first infinitesimal neighborhood of a linear configuration of points in $\mathbb P^2$ (2004)
Geramita, A. V., Migliore, J., Sabourin, L.
We consider the following open questions. Fix a Hilbert function, $h$, that occurs for a reduced zero-dimensional subscheme of $\mathbb P^2$. Among all subschemes, $X$, with Hilbert function $h$,...
The Weak and Strong Lefschetz Properties for Artinian K-Algebras (2002)
Harima, T., Migliore, J., Nagel, U., Watanabe, J.
Let A = bigoplus_{i >= 0} A_i be a standard graded Artinian K-algebra, where char K = 0. Then A has the Weak Lefschetz property if there is an element ell of degree 1 such that the multiplication...
Liaison and Related Topics: Notes from the Torino Workshop/School (2002)
These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the...
Ideals of general forms and the ubiquity of the Weak Lefschetz property (2002)
Migliore, J., Miró-Roig, R. M.
Let $d_1,...,d_r$ be positive integers and let $I = (F_1,...,F_r)$ be an ideal generated by general forms of degrees $d_1,...,d_r$, respectively, in a polynomial ring $R$ with $n$ variables. When all...
Bezout's theorem and Cohen-Macaulay modules (1999)
Migliore, J., Nagel, U., Peterson, C.
We define very proper intersections of modules and projective subschemes. It turns out that equidimensional locally Cohen-Macaulay modules intersect very properly if and only if they intersect...