A class of Gorenstein Artin algebras of embedding dimension four

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let R be a polynomial ring in n variables and I be a homogeneous ideal in R. Such an ideal I is called Gorenstein if the quotient R/I has a free resolution over R which is both self dual. In 2005 Iarrobino and Srinivasan (IS) proved a structure theorem for a class of Gorenstein Artin algebras of codimension four. We extend their results to establish the structure of another class of Gorenstein Artin algebras of Codimension four. In particular, if R is a polynomial ring in four variables and I is a Gorenstein ideal of height four whose degree two part I2 is generated by exactly three quadrics of height 1, then up to isomorphism I2 is either (wx,wy,wz) or (wx,wy,w2). The case (wx,wy,wz) is the one addressed by (IS) and we tackle the case of (wx,wy,w2) and give the structure and the minimal free resolution for a class of such ideals.