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 eprints
 Pub Date:
 October 2016
 arXiv:
 arXiv:1610.05794
 Bibcode:
 2016arXiv161005794F
 Keywords:

 Mathematics  Complex Variables;
 32E10;
 32H02;
 32Q45;
 14A10
 EPrint:
 In: Angella D., Medori C., Tomassini A. (eds) Complex and Symplectic Geometry, pp. 7384. Springer INdAM Series, vol 21. Springer, Cham (2017)