Louiza Fouli

WHAT IS A SYSTEM OF PARAMETERS

In this paper we discuss various refinements and generalizations of a theorem of Sankar Dutta and Paul Roberts. Their theorem gives a criterion for d elements in a d-dimensional Noetherian Cohen-Macaulay local ring to be a system of parameters, i.e., to have height d. We chiefly remove the assumption that the ring be Cohen-Macaulay and discuss similar theorems.

Rees algebras of square-free monomial ideals

We study the defining equations of the Rees algebra of square-free monomial ideals in a polynomial ring over a field. We determine that when an ideal

ANNIHILATORS OF GRADED COMPONENTS OF THE CANONICAL MODULE, AND THE CORE OF STANDARD GRADED ALGEBRAS

I

The cl-core of an ideal

is generated by

A formula for the *-core of an ideal

n

The core of ideals in arbitrary characteristic

square-free monomials of the same degree then

Chudnovsky's conjecture for very general points in PkN

I

A study on the core of ideals

has relation type at most

Chudnovsky's Conjecture for very general points in

n-2

\mathbb{P}_k^{N}

as long as