Göteborgs universitets publikationer

Weighted integral formulas on manifolds

Författare och institution:
Elin Götmark (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Arkiv för matematik, 46 ( 1 ) s. 43-68
ISSN:
00042080
Publikationstyp:
Publiceringsår:
2008
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
We present a method of finding weighted Koppelman formulas for $(p,q)$-forms on $n$-dimensional complex manifolds $X$ which admit a vector bundle of rank $n$ over $X \times X$, such that the diagonal of $X \times X$ has a defining section. We apply the method to $\Pn$ and find weighted Koppelman formulas for $(p,q)$-forms with values in a line bundle over $\Pn$. As an application, we look at the cohomology groups of $(p,q)$-forms over $\Pn$ with values in various line bundles, and find explicit solutions to the $\dbar$-equation in some of the trivial groups. We also look at cohomology groups of $(0,q)$-forms over $\Pn \times \Pm$ with values in various line bundles. Finally, we apply our method to developing weighted Koppelman formulas on Stein manifolds.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Nyckelord:
complex manifolds, integral representation, vanishing theorems
Postens nummer:
79569