Abstract We consider the dominant dimension of an order over a Cohen-Macaulay ring in category centrally modules. There is canonical tilting module case positive and we give upper bound on global its endomorphism ring.

The Chern numbers of the title are the first coefficients (after the multiplicities) of the Hilbert functions of various filtrations of ideals of a local ring (R, m). For a Noetherian (good) filtration A of m-primary ideals, the positivity and bounds for e1(A) are well-studied if R is Cohen-Macaulay, or more broadly, if R is a Buchsbaum ring or mild generalizations thereof. For arbitrary geomet...

The aim of this paper is to investigate properties of the local cohomology of rings of mixed characteristic that are analogous to Segre products of rings de ned over a eld. The main question is whether the local cohomology can be almost killed in a nite extension (we de ne what this means below). There are two reasons for considering this type of ring. First, there are special properties of the...

In this paper, we introduce the notion of “extension” of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being set theoretic complete intersection or arithmetically Cohen-Macaulay (Gorenstein) and having a Cohen-Macaulay tangent cone or a local ring with non-decreasing Hilbert function, from just one singl...

Inspired by the representation theory of rational Cherednik algebras, we consider whether certain rings corresponding to hyperplane arrangements in C satisfy the Cohen-Macaulay property. Specifically, for a partition λ = (λ1, . . . , λr) ` n we define a certain variety Xλ ⊂ C and study its coordinate ring C[Xλ]. The question which we work towards is: for which λ is Xλ CohenMacaulay? We consider...

We settle the negativity conjecture of Vasconcelos for the Chern number of an ideal in certain unmixed quotients of regular local rings by explicit calculation of the Hilbert polynomials of all ideals generated by systems of parameters. Introduction Let I be an m-primary ideal in a local ring (R,m) of dimension d. Let H(I, n) = λ(R/I) denote the Hilbert function of I where λ(M) denotes the leng...

Pinched Veronese rings are formed by removing an algebra generator from a subring of polynomial ring. We study the homological properties such rings, including Cohen-Macaulay, Gorenstein, and complete intersection properties. Greco Martino classified Cohen-Macaulayness pinched maximum entry exponent vector monomial; we re-prove their results with semigroup methods correct omission small class e...

Let H ⊆ Z be a positive semigroup generated by A ⊆ H, and let K[H] be the associated semigroup ring over a field K. We investigate heredity of the Cohen–Macaulay property from K[H] to both its A -Newton graded ring and to its face rings. We show by example that neither one inherits in general the Cohen–Macaulay property. On the positive side we show that for every H there exist generating sets ...

Let A be a Noetherian local ring with the maximal ideal m and d = dim A. Let Q be a parameter ideal in A. Let I = Q : m. The problem of when the equality I = QI holds true is explored. When A is a Cohen-Macaulay ring, this problem was completely solved by A. Corso, C. Huneke, C. Polini, and W. Vasconcelos [CHV, CP, CPV], while nothing is known when A is not a Cohen-Macaulay ring. The present pu...

We study Gorenstein dimension and grade of a module M over a filtered ring whose assosiated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a filtered module and its associated graded module is the most valuable property for an investigation of filtered rings. We prove an inequality G-dimM ≤ G-dimgrM and an equality gradeM = grade grM , whe...