ABSTRACT: In the 1960's, D.A. Buchsbaum constructed an equivariant finite free resolution of determinantal rings for the maximal minor case satisfying the conditions:
(1) The length of the resolution equals the projective dimension.
(2) Each term of the resolution is a finite direct sum of tensor products of exterior powers.
We prove, for arbitrary determinantal rings, the existence of an equivariant finite free resolution satisfying:
(1) The length of the resolution equals the projective dimension (n-t+1)(m-t+1), where n x m is the size of the generic matrix and t is the size of the minors.
(2) Each term of the resolution is a direct summand of a finite direct sum of tensor products of exterior powers.
If moreover R is local, then we can prove that there is a minimal one among such resolutions in the sense that it is a direct summand of any other such resolution.
 
 

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