Hilbert functions of Gorenstein algebras associated to a pencil of forms

摘要

Let R be a polynomial ring in r variables over an infinite field K, and denote by T> a corresponding dual ring, upon which R acts as differential operators We study type two graded level Artinian algebras A = R/I, having socle degree j. For each such algebra A, we consider the family of Artinian Gorenstein [AG] quotients of A having the same socle degree.