Holomorphic embeddings and immersions of Stein manifolds: a survey

Franc Forstneric

Holomorphic embeddings and immersions of Stein manifolds: a survey

Complex Variables 2018-10-03 v5 Algebraic Geometry Differential Geometry

Authors: Franc Forstneric

Abstract

In this paper we survey results on the existence of holomorphic embeddings and immersions of Stein manifolds into complex manifolds. Most results pertain to proper maps into Stein manifolds. We include a new result saying that every continuous map $X\to Y$ between Stein manifolds is homotopic to a proper holomorphic embedding provided that $\mathrm{dim} Y > 2\mathrm{dim}\, X$ and we allow a homotopic deformation of the Stein structure on $X$ .

Keywords

Stein manifold holomorphic embedding holomorphic immersion proper map complex manifold

Cite

@article{arxiv.1709.05630,
  title  = {Holomorphic embeddings and immersions of Stein manifolds: a survey},
  author = {Franc Forstneric},
  journal= {arXiv preprint arXiv:1709.05630},
  year   = {2018}
}

Comments

To appear in: J. Byun et al. (eds.), Geometric Complex Analysis (Proceedings of the KSCV12 Symposium, Gyeong-Ju, South Korea, 2017). Springer Proceedings in Mathematics & Statistics 246, https://doi.org/10.1007/978-981-13-1672-2_11

Holomorphic embeddings and immersions of Stein manifolds: a survey

Abstract

Keywords

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