Related papers: Rings of Teter type

A not necessarily noetherian local ring O is called regular if every finitely generated ideal I of O possesses finite projective dimension. In the article localizations O of a finitely presented, flat algebra A over a Pruefer domain R at a…

Let (R;m) be a numerical semigroup ring. In this paper we study the properties of its associated graded ring G(m). In particular, we describe the H^0_M for G(m) (where M is the homogeneous maximal ideal of G(m)) and we characterize when…

Let $\frak a$ be an ideal of a commutative noetherian ring $R$ with unity and $M$ an $R$-module supported at $\V(\fa)$. Let $n$ be the supermum of the integers $i$ for which $H^{\fa}_i(M)\neq 0$. We show that $M$ is $\fa$-cofinite if and…

Torus manifolds are topological generalization of smooth projective toric manifolds. We compute the rational cohomology ring of a class of smooth locally standard torus manifolds whose orbit space is a connected sum of simple polytopes.

We describe the equations of the Rees algebra R(I) of an equimultiple ideal I of deviation one, provided that I has a reduction J generated by a regular sequence and such that the initial forms of the elements of this sequence, except…

In this paper we describe the equations defining the multi-Rees algebra $R[I_1^{a_1}t_1,\dots,I_r^{a_r}t_r]$, where $R$ is a Noetherian ring and the ideals are generated by subsets of a fixed weak regular sequence.

We study normal compact K\"ahler spaces whose rational cohomology ring is isomorphic to that of a complex torus. We call them rational cohomology tori. We classify, up to dimension three, those with rational singularities. We then give…

On a (pseudo-)Riemannian manifold (M,g), some fields of endomorphisms i.e. sections of End(TM) may be parallel for g. They form an associative algebra A, which is also the commutant of the holonomy group of g. As any associative algebra, A…

Assume $R$ is a polynomial ring over a field and $I$ is a homogeneous Gorenstein ideal of codimension $g\ge3$ and initial degree $p\ge2$. We prove that the number of minimal generators $\nu(I_p)$ of $I$ that are in degree $p$ is bounded…

Quasi-socle ideals, that is the ideals $I$ of the form $I= Q : \mathfrak{m}^q$ in a Noetherian local ring $(A, \mathfrak{m})$ with the Gorenstein tangent cone $\mathrm{G}(\mathfrak{m}) = \bigoplus_{n \geq…

We show that in a polynomial ring $R$ in $N$ variables over an algebraically closed field $K$ of arbitrary characteristic, any $K$-subalgebra of $R$ generated over $K$ by at most $n$ forms of degree at most $d$ is contained in a…

A family of sets is intersecting if any two sets in the family intersect. Given a graph $G$ and an integer $r\geq 1$, let $\mathcal{I}^{(r)}(G)$ denote the family of independent sets of size $r$ of $G$. For a vertex $v$ of $G$, let…

The aim of this paper is to describe the topological $K$-ring, in terms of generators and relations, of a Springer variety $\mathcal{F}_{\lambda}$ of type $A$ associated to a nilpotent operator having Jordan canonical form whose block sizes…

Let $K$ be a number field with ring of integers $\mathcal{O}_K$ and let $G$ be a finite group. Given a $G$-Galois $K$-algebra $K_h$, let $\mathcal{O}_h$ denote its ring of integers. If $K_h/K$ is tame, then a classical theorem of E. Noether…

We extend rotation theory of circle maps to tiling spaces. Specifically, we consider a 1-dimensional tiling space $\Omega$ with finite local complexity and study self-maps $F$ that are homotopic to the identity and whose displacements are…

Let k be an arbitrary field and Q an acyclic quiver of tame type. Consider the path algebra kQ and the category of finite dimensional right modules Mod kQ. In the first part of the paper we deduce that the Gabriel-Roiter inclusions in…

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.…

Let R be a commutative ring with unit and let I be an ideal generated by a regular sequence. Then it is known that the natural sequences 0-> Tor_*^R(R/I,I^s)-> Tor_*^R(R/I,I^s/I^{s+1})-> Tor_{*-1}^R(R/I,I^{s+1})-> 0 are short exact…

Let $N$ be the smallest integer such that there is a non-tautological cohomology class of even degree on $\mathcal{\bar M}_{2,N}$. We remark that there is such a non-tautological class on $\mathcal{\bar M}_{2,20}$, by work of Graber and…

In a previous paper we exhibited the somewhat surprising property that most direct links of prime ideals in Gorenstein rings are equimultiple ideals with reduction number $1$. This led to the construction of large families of…