We study Cohen–Macaulayness, unmixedness, the structure of the canonical module
and the stability of the Hilbert function of algebraic residual intersections. We
establish some conjectures about these properties for large classes of residual
intersections without restricting the local number of generators of the ideals involved.
To determine the above properties, we construct a family of approximation complexes
for residual intersections. Moreover, we determine some general properties of the
symmetric powers of quotient ideals which were not known even for special ideals
with a small number of generators. Finally, we show acyclicity of a prime case of
these complexes to be equivalent to finding a common annihilator for higher Koszul
homologies, which unveils a tight relation between residual intersections and the
uniform annihilator of positive Koszul homologies, shedding some light on their
structure.
Instituto de Matemática
Universidade Federal do Rio de Janeiro
Av. Athos da Silveira Ramos 149
Centro de Tecnologia - Bloco C
Cidade Universitária - Ilha do Fundão
68530 21941-909 Rio de Janeiro
Brazil