Various approaches to products of residue currents

Abstract

We describe various approaches to Coleff-Herrera products of residue currents $R^j$ (of Cauchy-Fantappiè-Leray type) associated to holomorphic mappings $f_j$. More precisely, we study to which extent (exterior) products of natural regularizations of the individual currents $R^j$ yield regularizations of the corresponding Coleff-Herrera products. Our results hold globally on an arbitrary pure-dimensional complex space.

23 pages, rewritten introduction

References in corpus (3)

• Analytic continuation of residue currents
• Koppelman formulas and the $\dbar$-equation on an analytic space
• Residue currents associated with weakly holomorphic functions

Cited by in corpus (5)

• On a mixed Monge-Ampère operator for quasiplurisubharmonic functions with analytic singularities
• The $\bar{\partial }$-equation for $(p,q)$-forms on a non-reduced analytic space
• A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas
• Elementary construction of residue currents associated to Cohen-Macaulay ideals
• A residue calculus approach to the uniform Artin-Rees lemma