Residue currents associated with weakly holomorphic functions

Abstract

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, as 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.

28 pages. Updated with some corrections from the revision process. In particular, corrected and clarified some things in Section 5 and 6 regarding products of weakly holomorphic functions and currents, and the definition of the Bochner-Martinelli type currents

References in corpus (1)

• Analytic continuation of residue currents

Cited by in corpus (2)

• Various approaches to products of residue currents
• Residue currents with prescribed annihilator ideals on singular varieties