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Cohen-Macaulayness, unmixedness, the structure of the canonical module andthe stability of the Hilbert function of algebraic residual intersections arestudied in this paper. Some conjectures about these properties are establishedfor large classes of residual intersections without restricting local number ofgenerators of the ideals involved. A family of approximation complexes forresidual intersections is constructed to determine the above properties.Moreover some general properties of the symmetric powers of quotient ideals aredetermined which were not known even for special ideals with a small number ofgenerators. Acyclicity of a prime case of these complexes is shown to beequivalent to find a common annihilator for higher Koszul homologies. So that,a tight relation between residual intersections and the uniform annihilator ofpositive Koszul homologies is unveiled that sheds some light on theirstructure.

Residual Intersections and the Annihilator of Koszul Homologies