Holomorphically Equivalent Algebraic Embeddings

Peter Feller; Immanuel Stampfli

Holomorphically Equivalent Algebraic Embeddings

Algebraic Geometry 2014-10-17 v2 Complex Variables

Authors: Peter Feller , Immanuel Stampfli

Abstract

We prove that two algebraic embeddings of a smooth variety $X$ in $\mathbb{C}^m$ are the same up to a holomorphic coordinate change, provided that $2 \dim X + 1$ is smaller than or equal to $m$ . This improves an algebraic result of Nori and Srinivas. For the proof we extend a technique of Kaliman using generic linear projections of $\mathbb{C}^m$ .

Keywords

metric embeddings holomorphic mappings projective varieties

Cite

@article{arxiv.1409.7319,
  title  = {Holomorphically Equivalent Algebraic Embeddings},
  author = {Peter Feller and Immanuel Stampfli},
  journal= {arXiv preprint arXiv:1409.7319},
  year   = {2014}
}

Comments

17 pages. Version 2 acknowledges the fact that the main result of this paper was previously established by Kaliman, see http://arxiv.org/abs/1309.3791

Holomorphically Equivalent Algebraic Embeddings

Abstract

Keywords

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