On Products in a Family of Cohomology Theories Associated to the Invariant Prime Ideals of ... (BP).
On some properties of partial intersection schemes.
Partial intersection subschemes of Pr of codimension c were used to furnish various graded Betti numbers which agree with a fixed Hilbert function. Here we study some further properties of such schemes; in particular, we show that they are not in general licci and we give a large class of them which are licci. Moreover, we show that all partial intersections are glicci. We also show that for partial intersections the first and the last Betti numbers, say m and p respectively, give bounds each other;...
On Stanley-Reisner rings
On the Abel-Jacobi map for divisors of higher rank on a curve.
On the arithmetical rank of a special class of minimal varieties.
On the Betti numbers of perfect ideals
On the Castelnuovo-Mumford regularity of products of ideal sheaves.
On the Classification of Hermitian Forms. III. Complete Semilocal Rings.
On the Classification of Hermitian Forms. IV. Adele Rings.
On the Classification of Hermitian Forms. V. Global Rings.
On the Complexity of the Projective Classification of Surfaces.
On the computation of a-invariants.
On the computation of the minimal resolution of smooth parametric varieties.
On the depth and regularity of the symmetric algebra.
On the deviations of a local ring.
On the Dimension and Integrality of Symmetric Algebras.
On the ...-Dimension of Cartesian Squares.
On the endomorphism ring and Cohen-Macaulayness of local cohomology defined by a pair of ideals
Let , , be ideals of a Noetherian local ring . Let and be finitely generated -modules. We give a generalized version of the Duality Theorem for Cohen-Macaulay rings using local cohomology defined by a pair of ideals. We study the behavior of the endomorphism rings of and , where is the smallest integer such that the local cohomology with respect to a pair of ideals is nonzero and is the Matlis dual functor. We show that if is a -dimensional complete Cohen-Macaulay ring and ...
On the equivalence of algebraic and geometric local cohomology
In this paper, we will present several necessary and sufficient conditions on a commutative ring such that the algebraic and geometric local cohomologies are equivalent.
On the free character of the first Koszul homology module.
Let (A,M,K) denote a local noetherian ring A with maximal ideal M and residue field K. Let I be an ideal of A and E the Koszul complex generated over A by a system of generators of I.The condition: H1(E) is a free A/I-module, appears in several important results of Commutative Algebra. For instance:- (Gulliksen [3, Proposition 1.4.9]): The ideal I is generated by a regular sequence if and only if I has finite projective dimension and H1(E) is a free A/I-module.- (André [2]): Assume that A is a complete...