Associated graded algebra of a Gorenstein Artin algebra
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Bibliographic Information
Associated graded algebra of a Gorenstein Artin algebra
（Memoirs of the American Mathematical Society, no. 514）
American Mathematical Society, 1994
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"January 1994, volume 107, number 514 (third of 4 numbers)"
Includes bibliographical references (p. 105-108) and index
Description and Table of Contents
Description
In 1904, 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.
Table of Contents
Gorenstein Artin algebras and duality The intersection of two plane curves Extremal decompositions Components of the Hilbert scheme strata What decompositions $D$ and subquotients $Q(a)$ can occur? Relatively compressed Artin algebras Bibliography List of theorems, definitions, and examples Index.
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