Article contents
Hyperplanes of the Form f1(x, y)z1 + · · · + fk(x, y)zk + g(x, y) Are Variables
Published online by Cambridge University Press: 20 November 2018
Abstract
The Abhyankar–Sathaye Embedded Hyperplane Problem asks whether any hypersurface of ${{\mathbb{C}}^{n}}$ isomorphic to ${{\mathbb{C}}^{n-1}}$ is rectifiable, i.e., equivalent to a linear hyperplane up to an automorphism of ${{\mathbb{C}}^{n}}$. Generalizing the approach adopted by Kaliman, Vénéreau, and Zaidenberg, which consists in using almost nothing but the acyclicity of ${{\mathbb{C}}^{n-1}}$, we solve this problem for hypersurfaces given by polynomials of $\mathbb{C}\left[ x,y,{{z}_{1}},...,{{z}_{k}} \right]$ as in the title.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2005
References
- 1
- Cited by