A Class of Gorenstein Artin Algebras of Embedding Dimension Four

Abstract

In this article, we study height four graded Gorenstein ideals I in k[x, y, z, w] such that I 2 is of height one and generated by three quadrics. After a suitable linear change of variables, I ∩ k[x, y, z] is either Gorenstein or of type two. The former case was studied by Iarrobino and Srinivasan [8] where they give the structure of the ideal and its resolution. We study the latter case and give the structure of these ideals and their minimal resolution. We also explicitly write the form of the generators of I and the maps in the free resolution of R/I.