Related papers: Integrally closed ideals in two-dimensional regula…
We characterise ideals in two-dimensional regular local rings that arise as ideals of maximal minors of indecomposable integrally closed modules of rank two.
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 smooth complex variety can be realized as…
We characterise ideals in two-dimensional regular local rings that arise as ideals of maximal minors of indecomposable integrally closed modules of rank three.
Absolute integral closures of general commutative unital rings are explored. All rings admit absolute integral closures, but in general they are not unique. Among the reduced rings with finitely many minimal prime ideals, finite products of…
In this article we investigate when a complete ideal in a two-dimensional regular local ring is a multiplier ideal of some ideal with an integral multiplying parameter. In particular, we show that this question is closely connected to the…
The aim of this paper is to study jumping numbers and multiplier ideals of any ideal in a two-dimensional local ring with a rational singularity. In particular we reveal which information encoded in a multiplier ideal determines the next…
The aim of this paper is to study mixed multiplier ideals associated to a tuple of ideals in a two-dimensional local ring with a rational singularity. We are interested in the partition of the real positive orthant given by the regions…
In this article, we construct integrally closed modules of rank two over a two-dimensional regular local ring. The modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters. Then…
In this paper, we construct indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring. The modules are quite explicitly constructed from a given complete monomial ideal. We also give structural and…
Let R be an excellent local ring, m its maximal ideal and I an ideal. Then there exists a positive integer c such that for all integers n, the integral closure of (I + m^n) is contained in m^(n/c) + the integral closure of I. In the proof,…
In a formally unmixed Noetherian local ring, if the colength and multiplicity of an integrally closed ideal agree, then $R$ is regular. We deduce this using the relationship between multiplicity and various ideal closure operations.
Multiplier ideals, and the vanishing theorems they satisfy, have found many applications in recent years. In the global setting they have been used to study pluricanonical and other linear series on a projective variety. More recently, they…
In two dimensional regular local rings integrally closed ideals have a unique factorization property and have a Cohen-Macaulay associated graded ring. In higher dimension these properties do not hold for general integrally closed ideals and…
The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via…
Multiplicative hyperrings are an important class of algebraic hyperstructures which generalize rings further to allow multiple output values for the multiplication operation. Let R be a commutative multiplicative hyperring. The 2-prime…
Let $(A,\frak m)$ be an excellent normal local ring with algebraically closed residue class field. Given integrally closed $\frak m$-primary ideals $I\supset J$, we show that there is a composition series between $I$ and $J$, by integrally…
An ideal I of a commutative ring R is said to be irreducible if it cannot be written as the intersection of two larger ideals. A proper ideal I of a ring R is said to be strongly irreducible if for each ideals J, K of R, J\cap K\subseteq I…
It is shown that if $A$ is a regular local ring and $I$ is a maximally differential ideal in $A$, then $I$ is generated by an $A$-sequence.
In this article we investigate when a homogeneous ideal in a graded ring is normal, that is, when all positive powers of the ideal are integrally closed. We are particularly interested in homogeneous ideals in an N-graded ring generated by…
In this paper we investigate the question of normality for special monomial ideals in a polynomial ring over a field. We first include some expository sections that give the basics on the integral closure of a ideal, the Rees algebra on an…