Memoirs of the American Mathematical Society 1994; 115 pp; softcover Volume: 107 ISBN10: 0821825763 ISBN13: 9780821825761 List Price: US$36 Individual Members: US$21.60 Institutional Members: US$28.80 Order Code: MEMO/107/514
 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. Readership Research mathematicians. 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
