A structure theorem for type 3, grade 3 perfect ideals (Q1124637)

The purpose of this paper is to give a structure theorem for grade 3 perfect ideals of type 3 and defect \(\geq 2\) in a noetherian local ring (R,M,K). The starting point are two results of A. Brown, based, in their turn, on results of Buchsbaum, Eisenbud, Peskine and Szpiro. The first one provides a minimal projective resolution of \(J=(\bar x:I)\), starting from a minimal projective resolution of I, whenever I is a perfect ideal in a noetherian ring and \(\bar x\) is one of its maximal regular sequences. The second one gives a minimal set of generators and a minimal free resolution for a grade 3 almost complete intersection J of R, in terms of minors of an alternating matrix with entries in M. The author shows that if I is a grade 3 perfect ideal, with type\((I)=3\) and \(d(I)\geq 2\), which is not a complete intersection, then I is linked to an almost complete intersection of type n-3. Moreover, using some results from Weyman, he characterizes the multiplication on a minimal free resolution of such an \(I\quad mod(M).\) These tools enable him to produce a set of generators of I in terms of minors of two convenient matrices and to get a minimal free resolution of I, from a minimal free resolution of its linked ideal J.