Let $I$ be the ideal generated by alternating polynomials in two sets of $n$ variables. Haiman proved that the $q,t$-Catalan number is the Hilbert series of the graded vector space...
We provide explicit generators for the radical ideal defining the diagonal locus of $(\C^2)^n$ of certain bi-degrees. As a consequence, we discover a relation between $t,q$-Catalan numbers and...
The singularities of the principal component of the Hilbert scheme of points (2008)
We show that the principal component of the Hilbert scheme of 9 points in C^8 is not Cohen-Macaulay.
Syzygies of multiplier ideals on singular varieties (2008)
Lazarsfeld, Robert, Lee, Kyungyong, Smith, Karen E.
It was recently established by the first two authors that multiplier ideals on a smooth variety satisfy some special syzygetic properties. The purpose of this note is to show how some of these can be...
On the symmetric subscheme of Hilbert scheme of points (2007)
We consider the Hilbert scheme Hilb^{d+1}(C^d) of (d+1) points in affine d-space C^d (d > 2), which includes the square of any maximal ideal. We describe equations for the most symmetric affine open...
Characteristic 2 approach to bivariate interpolation problems (2007)
We investigate bivariate interpolation problems in characteristic 2. Given a nonnegative integer $t$, we describe all the sub-linear systems generated by monomials, in which there is no curve passing...
A short note on containment of cores (2007)
We show that cores of ideals do not preserve the inclusion.
Local syzygies of multiplier ideals (2006)
Lazarsfeld, Robert, Lee, Kyungyong
In recent years, multiplier ideals have found many applications in local and global algebraic geometry. Because of their importance, there has been some interest in the question of which ideals on a...
On the Realization of Line Arrangements as Multiplier Ideals.
We study the question of whether the ideal$I_r subset mathcal{O}_{C^3}$ of $r$ very general lines passing through the origin can be realized as a multiplier ideal. We show that when $r leq 10$,$I_r$...