The minimal free resolution of the Migliore-Peterson Rings in the case that the reflexive sheaf has even rank

Abstract. Let R be a commutative noetherian ring and ' : F! G be a homo-morphism of free R−modules where rank F = f and rank G = g. Fix an element bg+1 2 Vg+1 F and a generator!G for Vg G. The module action of V F onV F produces the element b1 = [(Vg ')(!G)] (bg+1) in F. Let J denote the image of b1: F ! R. Assume that grade J = f − g, which is the largest grade possible and is attained in the generic case. The ideal J may be interpreted as the dening ideal of the degeneracy locus of a regular section of a rank f − g reflexive sheaf. It may also be interpreted as the order ideal of an element in a second syzygy module of rank f − g. Also, J may be interpreted as the dening ideal for the symmetric algebra of a module of projective dimension two. Migliore and Peterson have studied the ideal Junm, which is the unmixed part of J. Under geometric hypotheses, they have shown that R=Junm is a Cohen-Macaulay ring and they have resolved this ring. Furthermore, if f − g is odd, then Junm is a Gorenstein ideal and is not equal to J. On the other hand, if f−g is even, then Junm = J. In the present paper, we produce the resolution of R=J by free R−modules in the case that f−g is even and (f−g−2)