PERFECT IDEALS OF GRADE THREE DEFINED BY SKEW-SYMMETRIZABLE MATRICES

Brown provided a structure theorem for a class of perfect ideals of grade 3 with type 2 and � > 0. We introduced a skew-symmetriz- able matrix to describe a structure theorem for complete intersections of grade 4 in a Noetherian local ring. We construct a class of perfect ideals I of grade 3 with type 2 defined by a certain skew-symmetrizable matrix. We present the Hilbert function of the standard k-algebras R/I, where R is the polynomial ring R = k(v0,v1,...,vm) over a field k with indeterminates vi and deg vi = 1.