Erzwingende Gleichung/Gerade/Beispiel/en

We consider the line  ${}X={\mathbb {A} }_{K}^{1}$  (or ${}X=K,\mathbb {R} ,{\mathbb {C} }$ etc.) with the (identical) function ${}x$. For  ${}f_{1}=x$  and  ${}f=0$,  i.e. for the homogeneous equation  ${}xt=0$,  the geometric object ${}V$ consists of a horizontal line (corresponding to the zero-solution) and a vertical line over  ${}x=0$.  So all fibers except one are zero-dimensional vector spaces. For the inhomogeneous equation  ${}xt=1$,  ${}T$ is a hyperbola, and all fibers are zero-dimensional with the exception that the fiber over  ${}x=0$  is empty.

For the homogeneous equation  ${}0t=0$,  ${}V$ is just the affine cylinder over the base line. For the inhomogeneous equation  ${}0t=x$,  ${}T$ consists of one vertical line, almost all fibers are empty.