Göteborgs universitets publikationer

# Residue currents on analytic spaces

Författare och institution:
Richard Lärkäng (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Utgiven i serie vid Göteborgs universitet:
Preprint - Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University, ISSN 1652-9715; nr 2010:20
Antal sidor:
60
Publikationstyp:
Licentiatavhandling
Förlagsort:
Göteborg
Publiceringsår:
2010
Språk:
engelska
Datum för examination:
2010-06-09
Tidpunkt för examination:
10:00
Lokal:
Pascal, Matematiska vetenskaper, Chalmers tvärgata 3, Göteborg
Opponent:
Prof. Alain Yger, Université Bordeaux 1, Frankrike
Fulltextlänk (lokalt arkiv):
Sammanfattning (abstract):

This thesis concerns residue currents on analytic spaces.

In the first paper, we construct Coleff-Herrera products and Bochner-Martinelli type currents associated with a weakly holomorphic mapping, and show that these currents satisfy well-known properties from the strongly holomorphic case. This includes the transformation law, the Poincaré-Lelong formula and the equivalence of the Coleff-Herrera product and the Bochner-Martinelli current associated with a complete intersection of weakly holomorphic functions.

In the second paper, we discuss the duality theorem on singular varieties. In the case of a complex manifold, the duality theorem, proven by Dickenstein-Sessa and Passare, says that the annihilator of the Coleff-Herrera product associated with a complete intersection $f$ equals the ideal generated by $f$. We give sufficient and in many cases necessary conditions in terms of certain singularity subvarieties of the sheaf $\mathcal{O}_Z$ for when the duality theorem holds on a singular variety $Z$.

Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Nyckelord:
analytic spaces, weakly holomorphic functions, residue currents, Coleff-Herrera products, the duality theorem
Postens nummer:
121457