Let $\Omega \subset \mathbb{C}^2$ be a pseudoconvex domain with real analytic boundary. We give conditions for the existence of a complex manifold $D$ and a branched, proper holomorphic mapping $f: \Omega \to D$. The essential point here is that $f$ is required to have nonempty branch locus. In the strongly pseudoconvex case, a criterion is given in terms of the Moser normal form. In the weakly pseudoconvex case, we introduce the class of "weakly spherical" domains which, generally speaking, are the most likely to possess branched mappings. We then produce the corrisponding normal form, which gives a necessary and sufficient condition for the existence of branched, proper mappings on weakly spherical domains
Existence of proper mappings from domains in $\mathbb{C}^2$
BARLETTA, Elisabetta;
1990-01-01
Abstract
Let $\Omega \subset \mathbb{C}^2$ be a pseudoconvex domain with real analytic boundary. We give conditions for the existence of a complex manifold $D$ and a branched, proper holomorphic mapping $f: \Omega \to D$. The essential point here is that $f$ is required to have nonempty branch locus. In the strongly pseudoconvex case, a criterion is given in terms of the Moser normal form. In the weakly pseudoconvex case, we introduce the class of "weakly spherical" domains which, generally speaking, are the most likely to possess branched mappings. We then produce the corrisponding normal form, which gives a necessary and sufficient condition for the existence of branched, proper mappings on weakly spherical domainsI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
