About the d-bar-equation at isolated singularities with regular exceptional set
| dc.creator | Ruppenthal, Jean | |
| dc.date | 2008-03-03 | |
| dc.date | 2009-03-23 | |
| dc.date.accessioned | 2026-07-07T12:54:36Z | |
| dc.date.available | 2026-07-07T12:54:36Z | |
| dc.description | Let Y be a pure dimensional analytic variety in C^n with an isolated singularity at the origin such that the exceptional set X of a desingularization of Y is regular. The main objective of this paper is to present a technique which allows to determine obstructions to the solvability of the d-bar-equation in the $L^2$ respectively $L^\infty$ sense on Y^*=Y-{0} in terms of certain cohomology classes on X. More precisely, let D be a Stein domain, relatively compact in Y, containing the origin, D^*=D-{0}. We give a sufficient condition for the solvability of the d-bar-equation in the $L^2$-sense on D^*; and in the $L^\infty$ sense, if D is in addition strongly pseudoconvex. If Y is an irreducible cone, we also give some necessary conditions and obtain optimal Hoelder estimates for solutions of the d-bar-equation. | |
| dc.description | 41 pages | |
| dc.identifier | https://arxiv.org/abs/0803.0152 | |
| dc.identifier | http://arxiv.org/abs/0803.0152 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223993 | |
| dc.subject | Complex Variables | |
| dc.subject | 32C36; 32W05 | |
| dc.title | About the d-bar-equation at isolated singularities with regular exceptional set | |
| dc.type | text |