A generic approach to the structure of certain normal ideals
A note on Rees algebras and the MFMC property.
An application of type sequences to the blowing-up.
An improved Briancon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras.
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...
Briançon-Skoda theorem for noetherian filtrations.
Clôture intégrale des idéaux et équisingularité
This text has two parts. The first one is the essentially unmodified text of our 1973-74 seminar on integral dependence in complex analytic geometry at the Ecole Polytechnique with J-J. Risler’s appendix on the Łojasiewicz exponents in the real-analytic framework. The second part is a short survey of more recent results directly related to the content of the seminar.The first part begins with the definition and elementary properties of the order function associated to an ideal of a reduced analytic...
Coassociated primes of modules over a commutative ring.
Cohen-Macaulay and Gorenstein property of rees algebras of non-singular equimultiple prime ideals.
Cohen-Macaulay Rees algebras and degrees of polynomial relations.
Cohen-Macauly Graphs.
Contractions of the actions of reductive algebraic groups in arbitrary characteristic.
C(X) vs. C(X) modulo its socle
Let be the socle of C(X). It is shown that each prime ideal in is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points. For each essential...
Erratum to: "C(X) vs. C(X) modulo its socle" (Colloq. Math. 111 (2008), 315-336)
Fiber cones and the integral closure of ideals.
Let (R,m) be a Noetherian local ring and let I C R be an ideal. This paper studies the question of when m I is integrally closed. Particular attention is focused on the case R is a regular local ring and I is a reduced ideal. This question arose through a question posed by Eisenbud and Mazur on the existence of evolutions.
Geometry of superficial elements
Graded rings of complete intersection local rings with finite residue fields.
Integral closures of ideals in the Rees ring
The important ideas of reduction and integral closure of an ideal in a commutative Noetherian ring A (with identity) were introduced by Northcott and Rees [4]; a brief and direct approach to their theory is given in [6, (1.1)]. We begin by briefly summarizing some of the main aspects.
Invariants of several matrices.