Related papers: Polar multiplicities and integral dependence
We lay out the theory of a multiplicity in the setting of a triangulated category having a central ring action from a graded-commutative ring $R$, in other words, an $R$-linear triangulated category. The invariant we consider is modelled on…
We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are…
The notion of multiplicity of a module first arose as consequence of Hilbert's work on commutative algebra, relating the dimension of rings with the degree of certain polynomials. For noncommutative rings, the notion of multiplicity first…
We consider the notion of mixed multiplicities for multigraded modules by using Hilbert series, and this is later applied to study the projective degrees of rational maps. We use a general framework to determine the projective degrees of a…
We introduce a spectrum for arbitrary varieties. This generalizes the definition by Steenbrink for hypersurfaces. In the isolated complete intersection singularity case, it coincides with the one given by Ebeling and Steenbrink except for…
This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate…
We establish the principle of specialization of integral dependence for submodules of finite colength of free modules, as part of the general algebraic-geometric theory of the Buchsbaum--Rim multiplicity. Then we apply the principle to the…
In this paper, we give a relation between the Hilbert multiplicity and the irreducible multiplicity. As an application, we characterize Ulrich modules in term of the irreducible multiplicity.
We offer new definitions of joint reductions and mixed Buchsbaum-Rim multiplicity for certain collections of modules over a Noetherian local ring and illustrate their application to give two different proofs of a joint-reduction-number-zero…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
Using invariants from commutative algebra to count geometric objects is a basic idea in singularities. For example, the multiplicity of an ideal is used to count points of intersection of two analytic sets at points of non-transverse…
A new criterion is developed which provides a check as to whether a chosen set of polarization observables is complete with respect to the determination of all independent $T$-matrix elements of a reaction of the type $a+b\to c+d+...$. As…
In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra theory to the foreground and promote its study. We…
We study algebraic points of bounded degree on polarized projective varieties. To do so, we refine further the filtration construction and Subspace Theorem approach, for the study of integral points, which has origins in the work of…
In this note we introduce higher order polar loci as natural generalizations of the classical polar loci, replacing the role of tangent spaces by that of higher order osculating spaces. The close connection between polar loci and dual…
We prove a projection formula, expressing a relative Buchsbaum--Rim multiplicity in terms of corresponding ones over a module-finite algebra of pure degree, generalizing an old formula for the ordinary (Samuel) multiplicity. Our proof is…
First, a new proof of Berman and Charpin's characterization of the Reed-Muller codes over the binary field or over an arbitrary prime field is presented. These codes are considered as the powers of the radical of a modular algebra.…
This paper is a review of concepts from graded commutative algebra with specific attention given to length and multiplicity. The author's motivation for this paper comes from the study of equivariant cohomology in algebraic topology where…
Let $ P(z) $ be a polynomial of degree $ n $ and for any real or complex number $\alpha,$ let $D_\alpha P(z)=nP(z)+(\alpha-z)P^{\prime}(z)$ denote the polar derivative with respect to $\alpha.$ In this paper, we obtain generalizations of…
In this note we compare the a-invariant of a homogeneous algebra B to the a-invariant of a subalgebra A. In particular we show that if $A \subset B$ is a finite homogeneous inclusion of standard graded domains over an algebraically closed…