Abstract
Given a submodule and a free resolution of J one can define a certain vector-valued residue current whose annihilator is J . We make a decomposition of the current with respect to Ass J that corresponds to a primary decomposition of J . As a tool we introduce a class of currents that includes usual residue and principal value currents; in particular these currents admit a certain type of restriction to analytic varieties and more generally to constructible sets.
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