CPL - Chalmers Publication Library

# A comparison formula for residue currents

Richard Lärkäng (Institutionen för matematiska vetenskaper, matematik)
(2012)
[Preprint]

Given two ideals $\mathcal{I}$ and $\mathcal{J}$ of holomorphic functions such that $\mathcal{I} \subseteq \mathcal{J}$, we describe a comparison formula relating the Andersson-Wulcan currents of $\mathcal{I}$ and $\mathcal{J}$. More generally, this comparison formula holds for residue currents associated to two generically exact complexes of vector bundles, together with a morphism between the complexes. We then show various applications of the comparison formula including generalizing the transformation law for Coleff-Herrera products to Andersson-Wulcan currents of Cohen-Macaulay ideals, proving that there exists a natural current $R^\mathcal{J}_Z$ on a singular variety $Z$ such that $\ann R^\mathcal{J}_Z = \mathcal{J}$, and giving an analytic proof of a theorem of Hickel related to the Jacobian determinant of a holomorphic mapping by means of residue currents.

CPL Pubid: 167860

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# Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)