Related papers: The Recursion Formula for Mixed Multiplicities wit…
This paper gives the additivity and reduction formulas for mixed multiplicities of multi-graded modules $M$ and mixed multiplicities of arbitrary ideals, and establishes the recursion formulas for the sum of all the mixed multiplicities of…
The original mixed multiplicity theory considered the class of mixed multiplicities concerning the terms of highest total degree in the Hilbert polynomial. This paper defines a broader class of mixed multiplicities that concern the maximal…
In the direction towards the question when mixed multiplicities are equal to the Hilbert-Samuel multiplicity of joint reductions, this paper not only generalizes [28, Theorem 3.1] that covers the Rees's theorem [13, Theorem 2.4], but also…
This paper defines the Euler-Poincar\'{e} characteristic of joint reductions of ideals which concerns the maximal terms in the Hilbert polynomial; characterizes the positivity of mixed multiplicities in terms of minimal joint reductions;…
Let S be a finitely generated standard multi-graded algebra over a Noetherian local ring A. This paper first expresses mixed multiplicities of S in term of Hilbert-Samuel multiplicity that explained the mixed multiplicities S as the…
Let $(A, \frak m)$ be a noetherian local ring with maximal ideal $\frak{m}$ and infinite residue field $k = A/\frak{m}.$ Let $J$ be an $\frak m$-primary ideal, $I_1,...,I_s$ ideals of $A$, and $M$ a finitely generated $A$-module. In this…
This paper establishes mixed multiplicity formulas concerning the relationship between mixed multiplicities of modules and mixed multiplicities of rings via rank of modules.
This paper shows that mixed multiplicities and the multiplicity of Rees modules of good filtrations and that of their reductions are the same. As an application of this result, we obtain interesting results on mixed multiplicities and the…
This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the computation of Milnor numbers of complex analytic hypersurfaces with isolated…
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 present a conjecture on multiplicity of irreducible representations of a subgroup $H$ contained in the irreducible representations of a group $G$, with $G$ and $H$ having the same derived groups. We point out some consequences of the…
Over a regular local ring of dimension two with maximal ideal m, we study the Buchsbaum-Rim multiplicity of a finitely generated module M of finite colength in a free module F. First, we investigate the colength of an m-primary ideal and…
We define a version of multiplier ideals, the Mather multiplier ideals, on a variety with arbitrary singularities, using the Mather discrepancy and the Jacobian ideal. In this context we prove a relative vanishing theorem, thus obtaining…
We show the existence (and define) the mixed multiplicities of arbitrary graded families of ideals under mild assumptions. In particular, our methods and results are valid for the case of arbitrary $\mathfrak{m}$-primary graded families.…
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.
In this paper, we prove the converse of Rees' mixed multiplicity theorem for modules, which extends the converse of the classical Rees' mixed multiplicity theorem for ideals given by Swanson - Theorem \ref{SwansonTheorem}. Specifically, we…
In this paper we improve drastically the estimate for the multiplicity of a binary recurrence. The main contribution comes from an effective version of the Faltings' Product Theorem.
A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This…
We introduce mixed Segre numbers of ideals which generalize the notion of mixed multiplicities of ideals of finite colength and show how many results on mixed multiplicities can be extended to results on mixed Segre numbers. In particular,…
We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the Laplace transform of the cut-and-join equation for the simple Hurwitz numbers. We show that the recursion recovers the Witten-Kontsevich theorem…