On the duality theorem on an analytic variety
Artikel i vetenskaplig tidskrift, 2013
The duality theorem for Coleff-Herrera products on a complex manifold says that
if $f = (f_1,\dots,f_p)$ defines a complete intersection, then the
annihilator of the Coleff-Herrera product $\mu^f$ 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 $\Ok_Z$.