Berechnung einiger Poincaré-Reihen
Betti numbers and the integral closure of ideals.
Bettireihen von Faserprodukten lokaler Ringe.
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.
Calculations about multiplicities.
One gives a formula for the calculation of the local intersection multiplicity index of analytic varieties, analogous to the Bézout formula in the case of algebraic varieties in the projective space, in the case of normal crossings. One obtains also a recurrent process for the calculation of the local intersection multiplicity index of plane analytic curves.
Castelnuovo Bounds for Certain Subvarieties in IPn.
Castelnuovo's index of regularity and reduction numbers
Castelnuovo's Regularity and Multiplicity.
Certain Complexes Associated to a Sequence and a Matrix.
Champs de vecteurs et formes différentielles sur une variété des points proches
Let be a smooth manifold, a local algebra in sense of André Weil, the manifold of near points on of kind and the module of vector fields on . We give a new definition of vector fields on and we show that is a Lie algebra over . We study the cohomology of -differential forms. Résumé. On considère une variété différentielle, une algèbre locale au sens d’André Weil, la variété des points proches de d’espèce et le module des champs de vecteurs sur . On donne une nouvelle...
Characterization of the Hilbert-Samuel polynomials of curve singularities
Characterizations of Buchsbaum Complexes.
Choosing Generators of Modules over Local Rings.
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...
Cohen-Macaulay and Gorenstein finitely graded rings