Reduction numbers, Rees algebras, and Pfaffian ideals<P>

I. Aberbach, S. Huckaba, C. Huneke<P>

Assuming that (R,m) is a Cohen-Macaulay local ring with
infinite residue field and I is an ideal of R having
analytic deviation 2, we provide a condition (in terms of 
a presentation matrix of I, and inspired by work of
Vasconcelos) that forces bounds 
on the reduction number of I. 
We proceed
to apply the condition 
to various situations.  Our main application is
to a certain family of
5-generated height 3 Gorenstein ideals of a regular local
ring.  This application is possible by making use 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-Macaulay Rees algebra
results.