Residue currents with prescribed annihilator ideals

Details Residue currents with prescribed annihilator ideals Residue currents with prescribed annihilator ideals

2005-11-09

arxiv.org/abs/math/0511237v3

Mathematics

Complex Variables

Scientific paper

Given a coherent ideal sheaf $J$ we construct locally a vector-valued residue current $R$ whose annihilator is precisely the given sheaf. In case $J$ is a complete intersection, $R$ is just the classical Coleff-Herrera product. By means of these currents we can extend various results, previously known for a complete intersection, to general ideal sheaves. Combining with integral formulas we obtain a residue version of the Ehrenpreis-Palamodov fundamental principle.

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