# Weighted integral formulas on manifolds Artikel i vetenskaplig tidskrift, 2008

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.

complex manifolds

vanishing theorems

integral representation

## Författare

### Elin Götmark

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

0004-2080 (ISSN)

Vol. 46 1 43-68

Matematik

### DOI

10.1007/s11512-007-0056-7

2017-10-07