Abstract view
Hyperplanes of the Form ${f_1(x,y)z_1+\dots+f_k(x,y)z_k+g(x,y)}$ Are Variables


Published:20051201
Printed: Dec 2005
Abstract
The AbhyankarSathaye Embedded Hyperplane Problem asks whe\ther any
hypersurface of $\C^n$ isomorphic to $\C^{n1}$ is rectifiable, {\em
i.e.,}
equivalent to a linear hyperplane up to an automorphism of $\C^n$.
Generalizing the approach adopted by Kaliman, V\'en\'ereau, and
Zaidenberg which
consists in using almost nothing but the acyclicity of $\C^{n1}$, we solve
this problem for hypersurfaces given by polynomials of $\C[x,y,z_1,\dots, z_k]$
as in the title.