Electronic ISBN:  9781470400910 
Product Code:  MEMO/107/514.E 
List Price:  $38.00 
MAA Member Price:  $34.20 
AMS Member Price:  $22.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 107; 1994; 115 ppMSC: Primary 13; Secondary 14; 58;
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.
ReadershipResearch mathematicians.

Table of Contents

Chapters

1. Gorenstein Artin algebras and duality: Intersection of the $m^i$ and the Löewy filtrations

2. The Intersection of two plane curves

3. Extremal decompositions

4. Components of the Hilbert scheme strata

5. What decompositions D and subquotients Q(a) can occur?

6. Relatively compressed Artin algebras


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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.
Research mathematicians.

Chapters

1. Gorenstein Artin algebras and duality: Intersection of the $m^i$ and the Löewy filtrations

2. The Intersection of two plane curves

3. Extremal decompositions

4. Components of the Hilbert scheme strata

5. What decompositions D and subquotients Q(a) can occur?

6. Relatively compressed Artin algebras