Holomorphic submersions from Stein manifolds
| dc.creator | Forstneric, Franc | |
| dc.date | 2003-09-05 | |
| dc.date | 2004-01-17 | |
| dc.date.accessioned | 2026-07-07T06:24:33Z | |
| dc.date.available | 2026-07-07T06:24:33Z | |
| dc.description | In this paper we prove results on the existence and homotopy classification of holomorphic submersions from Stein manifolds to other complex manifolds. We say that a complex manifold Y satisfies Property S_n for some integer n bigger or equal the dimension of Y if every holomorphic submersion from a compact convex set in C^n of a certain special type to Y can be uniformly approximated by holomorphic submersions from C^n to Y. Assuming this condition we prove the following. A continuous map f from an n-dimensional Stein manifold X to Y is homotopic to a holomorphic submersions of X to Y if and only if there exists a fiberwise surjective complex vector bundle map from TX to TY covering f. We also prove results on the homotopy classification of holomorphic submersions. We show that Property S_n is satisfied when n>dim Y and Y is any of the following manifolds: a complex Euclidean space, a complex projective space or Grassmanian, a Zariski open set in any of the above whose complement does not contain any complex hypersurfaces, a complex torus, a Hopf manifold, a non-hyperbolic Riemann surface, etc. In the case when Y is a complex Euclidean space the main result of this paper was obtained in [arXiv:math.CV/0211112]. | |
| dc.description | Annales Inst. Fourier, to appear | |
| dc.identifier | https://arxiv.org/abs/math/0309093 | |
| dc.identifier | http://arxiv.org/abs/math/0309093 | |
| dc.identifier | Ann. Inst. Fourier (Grenoble), 54 (2004), 1913--1942 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96581 | |
| dc.subject | Complex Variables | |
| dc.subject | 32E10, 32E30, 32H02 | |
| dc.title | Holomorphic submersions from Stein manifolds | |
| dc.type | text |