On the duality theorem on an analytic variety

Abstract

The duality theorem for Coleff-Herrera products on a complex manifold says that if f = (f1, . . ., fp) defines a complete intersection, then the annihilator of the Coleff-Herrera product μf equals (locally) the ideal generated by f. This does not hold unrestrictedly on an analytic variety Z. We give necessary, and in many cases sufficient conditions for when the duality theorem holds. These conditions are related to how the zero set of f intersects certain singularity subvarieties of the sheaf OZ. © 2012 Springer-Verlag.