REDUCTION NUMBERS, REES-ALGEBRAS AND PFAFFIAN IDEALS

Assuming that (R, m) is a Cohen-Macaulay local ring with infinite resi due field and I is an ideal of R having analytic deviation 2, we provi de a condition (in terms of a presentation matrix of I, and inspired b y work of Vasconcelos) that forces bounds on the reduction number of I . We proceed to apply the condition to various situations. Our main ap plication is to a certain family of 5-generated height 3 Gorenstein id eals of a regular local ring. This application is possible by making u se of the structure theorem of Buchsbaum and Eisenbud to express these Gorenstein ideals in terms of the Pfaffians of a 5 x 5 skew-symmetric presentation matrix of I. The applications help to produce Cohen-Maca ulay Rees algebra results.