Decomposition of residue currents

Details Decomposition of residue currents Decomposition of residue currents

2007-10-10

arxiv.org/abs/0710.2016v3

Mathematics

Complex Variables

Scientific paper

Given a submodule $J\subset \mathcal O_0^{\oplus r}$ 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 correspond 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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