Residue currents of monomial ideals

Journal article, 2007

We compute residue currents of Bochner-Martinelli type associated with a monomial ideal $I$, by methods involving certain toric varieties. In case the variety of $I$ is the origin, we give a complete description of the annihilator of the currents in terms of the associated Newton diagram. In particular, we show that the annihilator is strictly included in $I$, unless $I$ is defined by a complete intersection.