Residual Intersections are Koszul-Fitting ideals

Abstract

One describes generators of disguised residual intersections in any commutative Noetherian rings. It is shown that, over Cohen-Macaulay rings, the disguised residual intersections and algebraic residual intersections are the same, for ideals with sliding depth. This coincidence provides structural results for algebraic residual intersections in quite general setting. It is shown how the DG-algebra structure of Koszul homologies affects the determination of generators of residual intersections. In the midway it is shown that the Buchsbaum-Eisenbud family of complexes can be derived from the Koszul-Čech spectral sequence. This interpretation of Buchsbaum-Eisenbud families has crucial rule to establish the above results.

32pages, Comments Welcome \\ V2: Besides the improvement of the expositions of Sections 3 and 4, we prove our conjecture 5.7 in the case where $s\le g+1$. Now, one knows the structure of $s\le g+1$-residual intersections in any (Cohen-Macaulay) rings