# On the duality theorem on an analytic variety Journal article, 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 $\Ok_Z$.

## Author

### Richard Lärkäng

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

#### Mathematische Annalen

0025-5831 (ISSN) 1432-1807 (eISSN)

Vol. 355 1 215-234

### Subject Categories

Mathematics

Mathematical Analysis

Basic sciences

### DOI

10.1007/s00208-012-0782-4