相关论文: Elimination and nonlinear equations of Rees algebr…
The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
This paper shows among other things that over a non-commutative Koszul algebra, high truncations of finitely generated graded modules have linear free resolutions.
Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is…
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated and that such an…
Some general criteria to produce explicit free algebras inside the division ring of fractions of skew polynomial rings are presented. These criteria are applied to some special cases of division rings with natural involutions, yielding, for…
In this paper, we study arithmetic Macaulayfication of projective schemes and Rees algebras of ideals. We give a necessary and sufficient condition for a nonsingular projective scheme to have an arithmetic Macaulayfication. If the scheme is…
Based on a theorem by Vasconcelos, we give an algorithm for equidimensional decomposition of algebraic sets using syzygy computations via Gr\"obner bases. This algorithm avoids the use of elimination, homological algebra and processing the…
We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting. We give an application to…
We describe the progress in the last 10 years related to Koszul modules and syzygies of algebraic varieties. Topics discussed include the general theory of Koszul modules and resonance varieties, applications to Chen ranks of K\"ahler and…
In a vertex algebra setting, we consider non-local screening operators associated to the basis of any non-integral lattice. We have previously shown that, under certain restrictions, these screening operators satisfy the relations of a…
Given two determinantal rings over a field k. We consider the Rees algebra of the diagonal ideal, the kernel of the multiplication map. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the join variety.…
The full lattice convergence on a locally solid Riesz space is an abstraction of the topological, order, and relatively uniform convergences. We investigate four modifications of a full convergence $\mathbb{c}$ on a Riesz space. The first…
This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex Poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex Poisson algebra are revisited and certain general…
The rate of a standard graded $K$-algebra $A$ is a measure of the growth of the shifts in a minimal free resolution of $K$ as an $A$-module. In particular $A$ has rate one if and only if it is Koszul. It is known that a generic Artinian…
It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance $\epsilon>0$ and an $\epsilon$-irreducible algebraic affine plane curve $\mathcal C$ of…
This note gives the complete projective classification of rational, cuspidal plane curves of degree at least 6, and having only weighted homogeneous singularities. It also sheds new light on some previous characterizations of free and…
For $\mathcal{O}$ a reduced operad, a generalized divergence from the derivations of a free $\mathcal{O}$-algebra to a suitable trace space is constructed. In the case of the Lie operad, this corresponds to Satoh's trace map and, for the…
We introduce the notion of a complex cell, a complexification of the cells/cylinders used in real tame geometry. For $\delta\in(0,1)$ and a complex cell $\mathcal{C}$ we define its holomorphic extension…
We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define…