On the free resolutions of local cohomology modules with respect to an ideal generated by a U.S. D-sequence
On the Grade of Some Ideals.
On the graded Betti numbers for large finite subsets of curves
We prove a recent conjecture of S. Lvovski concerning the periodicity behaviour of top Betti numbers of general finite subsets with large cardinality of an irreducible curve C ⊂ ℙⁿ.
On the grades of order ideals.
On the Hilbert function of curvilinear zero-dimensional subschemes of projective spaces
Here we show the existence of strong restrictions for the Hilbert function of zerodimensional curvilinear subschemes of P n with one point as support and with high regularity index.
On the homogeneous ideal of unreduced projective schemes.
On the homogeneous pieces of graded generalized local cohomology modules
We study, in certain cases, the notions of finiteness and stability of the set of associated primes and vanishing of the homogeneous pieces of graded generalized local cohomology modules.
On the homology of some special complexes. (Sobre la homología de algunos complejos especiales.)
On the ... in a minimal injective resolution II.
On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence
Let be a local ring and a semidualizing module of . We investigate the behavior of certain classes of generalized Cohen-Macaulay -modules under the Foxby equivalence between the Auslander and Bass classes with respect to . In particular, we show that generalized Cohen-Macaulay -modules are invariant under this equivalence and if is a finitely generated -module in the Auslander class with respect to such that is surjective Buchsbaum, then is also surjective Buchsbaum.
On the Jacobian ideal of the binary discriminant.
Let Δ denote the discriminant of the generic binary d-ic. We show that for d ≥ 3, the Jacobian ideal of Δ is perfect of height 2. Moreover we describe its SL2-equivariant minimal resolution and the associated differential equations satisfied by Δ. A similar result is proved for the resultant of two forms of orders d, e whenever d ≥ e-1. If Φn denotes the locus of binary forms with total root multiplicity ≥ d-n, then we show that the ideal of Φn is also perfect, and we construct a covariant which...
On the length of the absolute Samuel stratum
On the minimal reduction and multiplicity of .
On the minimaxness and coatomicness of local cohomology modules
Let be a commutative Noetherian ring, an ideal of and an -module. We wish to investigate the relation between vanishing, finiteness, Artinianness, minimaxness and -minimaxness of local cohomology modules. We show that if is a minimax -module, then the local-global principle is valid for minimaxness of local cohomology modules. This implies that if is a nonnegative integer such that is a minimax -module for all and for all , then the set is finite. Also, if is minimax for...
On the non-vanishing of cotangent cohomology.
On the non-vanishing of local cohomology modules
It is shown that for any Artinian modules , is the greatest integer such that .
On the partial Euler-Poincare characteristics of certain systems of parameters in local rings.
On the Poincaré series for a plane divisorial valuation.
On the regularity and defect sequence of monomial and binomial ideals
When is a polynomial ring or more generally a standard graded algebra over a field , with homogeneous maximal ideal , it is known that for an ideal of , the regularity of powers of becomes eventually a linear function, i.e., for and some integers , . This motivates writing for every . The sequence , called the defect sequence of the ideal , is the subject of much research and its nature is still widely unexplored. We know that is eventually constant. In this article, after...
On the Steenrod operations in cyclic cohomology.