See our librarian page for additional eBook ordering options. In , Macaulay described the Hilbert function of the intersection of two plane curve branches: It is the sum of a sequence of functions of simple form. This monograph describes the structure of the tangent cone of the intersection underlying this symmetry.
Iarrobino generalizes Macaulay's result beyond complete intersections in two variables to Gorenstein Artin algebras in an arbitrary number of variables. He shows that the tangent cone of a Gorenstein singularity contains a sequence of ideals whose successive quotients are reflexive modules. Applications are given to determining the multiplicity and orders of generators of Gorenstein ideals and to problems of deforming singular mapping germs.
Also included are a survey of results concerning the Hilbert function of Gorenstein Artin algebras and an extensive bibliography. AMS Homepage. Join our email list. Sign up. On the structure of certain normal ideals. Local properties of licci ideals. On the multiplicity of blow-up rings of ideals generated by d -sequences.
Algebra , 80 3 , Remarks on residual intersections. Notes Math. Jones and Bartlett, Boston, MA, Kustin and Bernd Ulrich.
If the socle fits. Kustin, Matthew Miller, and Bernd Ulrich. Generating a residual intersection. A family of complexes associated to an almost alternating map, with applications to residual intersections.
Herzog, B. Ulrich, and J. Linear maximal Cohen-Macaulay modules over strict complete intersections. Algebra , 71 , Self-linked curve singularities. Nagoya Math. Generic residual intersections.
Springer, Berlin, Sums of linked ideals. Powers of licci ideals. Springer, New York, On licci ideals.
Residual intersections. Algebraic linkage. Duke Math. Minimal linkage and the Gorenstein locus of an ideal. Theory and applications of universal linkage. Pure Math.
Associated Graded Algebra of a Gorenstein Artin Algebra cover image. Memoirs of the American Mathematical Society ; pp;. , English, Book, Illustrated edition: Associated graded algebra of a Gorenstein Artin algebra / Anthony A. Iarrobino. Iarrobino, Anthony A. (Anthony Ayers).
North-Holland, Amsterdam, Maximally generated Cohen-Macaulay modules. Vanishing of cotangent functors. The structure of linkage. Linkage and compressed algebras. Linkage theory for algebras with pure resolutions.
Rings of invariants and linkage of determinantal ideals. Liaison and deformation. Algebra , 39 , Divisor class groups and deformations. Gorenstein rings and modules with high numbers of generators. In Algebra. Joint paper with G.
Casnati, R. Notari and M. Isomorphism classes of short Gorenstein local rings via Macaulay's inverse system. Volume , Number 9, September , Pages — Joint paper with M. On the asymptotic depth of multigraded modules. Isomorphism classes of certain Gorenstein ideals. Algebra and Representation Theory Hilbert polynom ial under liaison: the local case. Contemporary Mathematics , Joint paper with J. Structure theorems for certain Gorenstein ideals. Special volume in honor of Melvin Hochster.
Michigan Journal of Math. Upper bounds of Hilbert coefficients and Hilbert functions.
A moduli scheme of curve singularities. Bigraded structures and the depth of blow-up algebras. Proceedings of the Royal Soc. On the first normalized Hilbert coefficient. The depth of the higher associated graded ring. London Math. On the computation of Ratliff-Rush closure.
Symbolic Computation 37 , Two results on the number of generators. Hilbert function and fractional powers.
The zero-dimensional case had been studied by Macaulay Simis, C. Join our email list. Marcos, R. However, in the connected case, we have a quite simpler proof.