Elizabeth Wulcan

Decomposition of residue currents

Abstract Given a submodule and a free resolution of J one can define a certain vector-valued residue current whose annihilator is J. We make a decomposition of the current with respect to Ass J that corresponds to a primary decomposition of J. As a tool we introduce a class of currents that includes usual residue and principal value currents; in particular these currents admit a certain type of restriction to analytic varieties and more generally to constructible sets.

Computing residue currents of monomial ideals using comparison formulas

Given a free resolution of an ideal a of holomorphic functions, one can construct a vector-valued residue current R, which coincides with the classical Coleff–Herrera product if a is a complete intersection ideal and whose annihilator ideal is precisely a. We give a complete description of R in the case when a is an Artinian monomial ideal and the resolution is the hull resolution (or a more general cellular resolution). The main ingredient in the proof is a comparison formula for residue currents due to the first author. By means of this description, we obtain in the monomial case a current version of a factorization of the fundamental cycle of a due to Lejeune-Jalabert.

Green functions, Segre numbers, and King’s formula

Let

Some variants of Macaulay's and Max Noether's theorems

\mathcal J

One parameter regularizations of products of residue currents

be a coherent ideal sheaf on a complex manifold

Residue Currents and Fundamental Cycles

X

Variants of the Effective Nullstellensatz and Residue Calculus

with zero set

On the effective membership problem for polynomial ideals

Z

Residue currents with prescribed annihilator ideals

, and let

Degree growth of monomial maps and McMullen's polytope algebra

G