Surjective holomorphic maps onto Oka manifolds
Abstract
Let $X$ be a connected Oka manifold, and let $S$ be a Stein manifold with $\mathrm{dim} S \geq \mathrm{dim} X$. We show that every continuous map $S\to X$ is homotopic to a surjective strongly dominating holomorphic map $S\to X$. We also find strongly dominating algebraic morphisms from the affine $n$-space onto any compact $n$-dimensional algebraically subelliptic manifold. Motivated by these results, we propose a new holomorphic flexibility property of complex manifolds, the basic Oka property with surjectivity, which could potentially provide another characterization of the class of Oka manifolds.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2016
- DOI:
- 10.48550/arXiv.1610.05794
- arXiv:
- arXiv:1610.05794
- Bibcode:
- 2016arXiv161005794F
- Keywords:
-
- Mathematics - Complex Variables;
- 32E10;
- 32H02;
- 32Q45;
- 14A10
- E-Print:
- In: Angella D., Medori C., Tomassini A. (eds) Complex and Symplectic Geometry, pp. 73-84. Springer INdAM Series, vol 21. Springer, Cham (2017)