Till sidans topp

Sidansvarig: Webbredaktion

A comparison formula for… - Göteborgs universitet Till startsida
Webbkarta
Till innehåll Läs mer om hur kakor används på gu.se

# A comparison formula for residue currents

Övrigt
Författare Richard Lärkäng 2012 Institutionen för matematiska vetenskaper, matematik en arxiv.org/abs/1207.1279 arxiv.org/pdf/1207.1279 Algebra och geometri, Matematisk analys

## Sammanfattning

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.