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Residue currents associated with weakly holomorphic functions. (English) Zbl 1269.32001

Summary: We construct Coleff-Herrera products and Bochner-Martinelli type residue currents associated with a tuple \(f\) of weakly holomorphic functions, and show that these currents satisfy basic properties from the (strongly) holomorphic case. This includes the transformation law, the Poincaré-Lelong formula, and the equivalence of the Coleff-Herrera product and the Bochner-Martinelli type residue current associated with \(f\) when \(f\) defines a complete intersection.

MSC:

32A27 Residues for several complex variables
32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)
32C30 Integration on analytic sets and spaces, currents
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