Weighted integral formulas on manifolds
| dc.creator | Götmark, Elin | |
| dc.date | 2006-11-03 | |
| dc.date.accessioned | 2026-07-07T09:43:26Z | |
| dc.date.available | 2026-07-07T09:43:26Z | |
| dc.description | 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. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611082 | |
| dc.identifier | http://arxiv.org/abs/math/0611082 | |
| dc.identifier | Ark. Mat., 46 (2008), 43--68 | |
| dc.identifier | doi:10.1007/s11512-007-0056-7 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162555 | |
| dc.subject | Complex Variables | |
| dc.subject | 32A26; 32Q99; 32Q28 | |
| dc.title | Weighted integral formulas on manifolds | |
| dc.type | text |