An improved Briancon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras.
Aritmética de los semigrupos de Arf y saturados. Aplicaciones.
Artin Approximation and Formal Fibres of Local Rings.
Artin-Nagata properties and Cohen-Macaulay associated graded rings
Associated graded rings and connected sums
In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring , which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincaré...
Associated Graded Rings Derived from Integrally Closed Ideals and the Local Homological Conjectures
Bass numbers and Golod rings.
Berechnung einiger Poincaré-Reihen
Bounds for the multiplicity of almost complete intersections.
Bounds on Bass numbers and their dual
Let be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated -module.
Bounds on Castelnuovo-Mumford regularity for divisors on rational normal scrolls.
The Castelnuovo-Mumford regularity is one of the most important invariants in studying the minimal free resolution of the defining ideals of the projective varieties. There are some bounds on the Castelnuovo-Mumford regularity of the projective variety in terms of the other basic invariants such as dimension, codimension and degree. This paper studies a bound on the regularity conjectured by Hoa, and shows this bound and extremal examples in the case of divisors on rational normal scrolls.
Bounds on Castelnuovo-Mumford regularity for generalized Cohen-Macaulay graded rings.
Castelnuovo Bounds for Certain Subvarieties in IPn.
Castelnuovo's Regularity and Multiplicity.
Certain Complexes Associated to a Sequence and a Matrix.
Characterization of the Hilbert-Samuel polynomials of curve singularities
Characterizations of Buchsbaum Complexes.
Classification of the Tor-Algebras of Codimension Four Gorenstein Local Rings
Codimesion two linear varieties with nilpotent structures.
Cohen-Lenstra sums over local rings
We study series of the form , where is a commutative local ring, is a non-negative integer, and the summation extends over all finite -modules , up to isomorphism. This problem is motivated by Cohen-Lenstra heuristics on class groups of number fields, where sums of this kind occur. If has additional properties, we will relate the above sum to a limit of zeta functions of the free modules , where these zeta functions count -submodules of finite index in . In particular we will show that...