Related papers: Valuation spaces and multiplier ideals on singular…
The primary goal of this paper is to provide a general multiplicity estimate. Our main theorem allows to reduce a proof of multiplicity lemma to the study of ideals stable under some appropriate transformation of a polynomial ring. In…
We show how suitable extensions $(L|K,v)$ of prime degree of valued fields give rise to definable coarsenings of the valuation rings of $L$ and $K$. In the case of Artin-Schreier and Kummer extensions with wild ramification, we can also…
Classically, Groebner bases are computed by first prescribing a set monomial order. Moss Sweedler suggested an alternative and developed a framework to perform such computations by using valuation rings in place of monomial orders. We build…
This is the first part of a series of articles where we are going to develop theory of valuations on manifolds generalizing the classical theory of continuous valuations on convex subsets of a linear space. In this article we still work…
We develop the theory of Gr\"obner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division…
Thompson (2014) exhibits a formula for the multiplier ideal with multiplier lambda of a monomial curve C with ideal I as an intersection of a term coming from the I-adic valuation, the multiplier ideal of the term ideal of I, and terms…
In this paper, we give a valuation formula for rational top differential forms of function fields in characteristic zero for arbitrary Abhyankar places generalizing the classical valuation at prime divisors. This enables us to define log…
We associate a family of ideal sheaves to any Q-effective divisor on a complex manifold, called higher multiplier ideals, using the theory of mixed Hodge modules and V-filtrations. This family is indexed by two parameters, an integer…
We study existence and computability of finite bases for ideals of polynomials over infinitely many variables. In our setting, variables come from a countable logical structure A, and embeddings from A to A act on polynomials by renaming…
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…
The notions of $\mathbb Q$-Gorenstein scheme and of $\mathbb Q$-Gorenstein morphism are introduced for locally Noetherian schemes by dualizing complexes and (relative) canonical sheaves. These cover all the previously known notions of…
We study $F$-graded systems of ideals in $R$, which are sequences of ideals giving rise to Cartier algebras on $R$. We identify how properties of these systems (or modifications of these systems) affect the singularity properties of the…
Given an affine algebraic variety V and a quantization A of its coordinate ring, it is conjectured that the primitive ideal space of A can be expressed as a topological quotient of V. Evidence in favor of this conjecture is discussed, and…
The concept of variety with IBN (invariant basic number) propriety first appeared in ring theory. But we can define this concept for arbitrary variety of universal algebras with arbitrary signature; see Definition 1.4. The proving of the…
The purpose of the present work is to describe a dequantization procedure for topological modules over a deformed algebra. We define the characteristic variety of a topological module as the common zeroes of the annihilator of the…
In this paper we make a systematic study of the multiplicity of the jumping points associated to the mixed multiplier ideals of a family of ideals in a complex surface with rational singularities. In particular we study the behaviour of the…
In this paper we define and explore properties of mixed multiplicities of (not necessarily Noetherian) filtrations of $m_R$-primary ideals in a Noetherian local ring $R$, generalizing the classical theory for $m_R$-primary ideals. We…
We give a survey on b-function, spectrum, and multiplier ideals together with certain interesting relations among them including the case of arbitrary subvarieties.
We classify all Q-factorializations of (co)minuscule Schubert varieties by using their Mori dream space structure. As a corollary we obtain a description of all IH-small resolutions of (co)minuscule Schubert varieties generalizing results…
We introduce a new variant of tight closure associated to any fixed ideal $\a$, which we call $\a$-tight closure, and study various properties thereof. In our theory, the annihilator ideal $\tau(\a)$ of all $\a$-tight closure relations,…