Holomorphically Equivalent Algebraic Embeddings

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 ${\mathbb{C}}^m$.

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