相关论文: Multiplicity $=$ Volume formula and Newton non-deg…

We present a package 'MixedMultiplicity' for computing mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over a field. This enables us to find mixed volumes of convex lattice polytopes…

We find simple necessary and sufficient conditions on a local ring $R$ of dimension $d$ for the limit $$ \lim_{i\rightarrow\infty}\frac{\ell_R(R/I_n)}{n^d} $$ to exist whenever $\{I_n\}$ is a graded family of $m_R$-primary ideals, and give…

We develop a theory of multiplicities and mixed multiplicities of filtrations, extending the theory for filtrations of $m$-primary ideals to arbitrary (not necessarily Noetherian) filtrations. The mixed multiplicities of $r$ filtrations on…

Let $(R, \mathfrak m)$ be a Noetherian local ring and $I$ a $\mathfrak m$-primary ideal. In this paper, we study an inequality involving the number of generators, the Loewy length and the multiplicity of $I$. There is strong evidence that…

In this article we extend a previous definition of Castelnuovo-Mumford regularity for modules over an algebra graded by a finitely generated abelian group. Our notion of regularity is based on Maclagan and Smith's definition, and is…

Continuing a well established tradition of associating convex bodies to monomial ideals, we initiate a program to construct asymptotic Newton polyhedra from decompositions of monomial ideals. This is achieved by forming a graded family of…

Let $R$ be a standard graded polynomial ring that is finitely generated over a field of characteristic $0$, let $\mathfrak{m}$ be the homogeneous maximal ideal of $R$, and let $I$ be a homogeneous prime ideal of $R$. Dao and Monta\~{n}o…

We give an effective method to determine the multiplier ideals and jumping numbers associated with a curve singularity $C$ in a smooth surface. We characterize the multiplier ideals in terms of certain Newton polygons, generalizing a…

We introduce two new invariants of a Noetherian (standard graded) local ring $(R, \mathfrak m)$ that measure the number of generators of certain kinds of reductions of $\mathfrak m,$ and we study their properties. Explicitly, we consider…

We introduce the notion of integrality of Grothendieck categories as a simultaneous generalization of the primeness of noncommutative noetherian rings and the integrality of locally noetherian schemes. Two different spaces associated to a…

Let $(R,\mathfrak{m})$ be a Noetherian local ring and $M$ a finitely generated $R$-module. We study the relations of the index of reducibility and the irreducible multiplicity of an $\mathfrak{m}$-primary ideal of $R$ and these of…

We associate convex regions in R^n to m-primary graded sequences of subspaces, in particular m-primary graded sequences of ideals, in a large class of local algebras (including analytically irreducible local domains). These convex regions…

Let R be a Noetherian standard graded ring, and M and N two finitely generated graded R-modules. We introduce reg_R (M,N) by using the notion of generalized local cohomology instead of local cohomology, in the definition of regularity. We…

We give several new applications of our theorem on the existence of multiplicity of graded families of ideals as a limit, including a very general Minkowski type inequality for graded families of ideals, a very general formula for existence…

Let $(\mathcal{O}_n, \mathfrak{m})$ denote the ring of germs of holomorphic functions $\mathbb{C}^n\to \mathbb{C}$, and let $I\subseteq \mathcal{O}_n$ be an $\mathfrak{m}$-primary ideal. Demailly and Pham showed that $\mathrm{lct}(I) \geq…

We compute the $F$-pure threshold of some non-principal ideals which satisfy a geometric generic condition about their Newton polyhedron. We also contribute some evidence in favor of the conjectured equality between the $F$-pure threshold…

In 2007, Y. Shimoda, in connection with a long-standing question of J. Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal are complete intersections, has Krull dimension at most…

Let $(R, \mathfrak{m})$ be a Noetherian local ring. This paper concerns several extremal invariants arising from the study of the relation between colength and (Hilbert--Samuel or Hilbert--Kunz) multiplicity of an $\mathfrak{m}$-primary…

We prove a characterization of the j-multiplicity of a monomial ideal as the normalized volume of a polytopal complex. Our result is an extension of Teissier's volume-theoretic interpretation of the Hilbert-Samuel multiplicity for m-primary…

Let (RmR), (SmS) and (TmT) be Noetherian local rings sharing the same residue eld k and prime characteristic p > 0. We establish some formulas relating the h-function and s-multiplicity of the ber product R T S in terms of the h-functions…