Associated Graded Algebra of a Gorenstein Artin Algebra

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 intersections underlying this symmetry. Iarrobino generalizes Macaulay's result beyond complete intersections intwo variable to Gorenstein Artin algebras in an arbitary number of variables. He shows that the tangent cone of a Gorenstein singulairty 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.Iarrobino, Anthony A. is the author of 'Associated Graded Algebra of a Gorenstein Artin Algebra' with ISBN 9780821825761 and ISBN 0821825763.