CPL - Chalmers Publication Library

# Weighted integral formulas on manifolds

Elin Götmark (Institutionen för matematiska vetenskaper, matematik)
Arkiv för matematik (00042080). Vol. 46 (2008), 1, p. 43-68.

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.

Nyckelord: complex manifolds, integral representation, vanishing theorems

CPL Pubid: 79569

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# Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)