A DG ALGEBRA RESOLUTION OF TRIMMINGS OF GORENSTEIN IDEALS

. Let ( R, m , k ) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that I is generated by the sub-maximal pfaffians of this matrix. Let J be the ideal obtained by multiplying some of the pfaffian generators of I by m ; we say that J is a trimming of I . In this paper we construct an explicit free resolution of R/J with a DG algebra structure. Our work builds upon a recent paper of Vandebogert. We use our DG algebra resolution to prove that recent conjectures of Christensen, Veliche and Weyman on ideals of class G hold true in our context and to address the realizability question for ideals of class G .