Erzwingende Gleichung/Gerade/Beispiel/en

We consider the line  $X={𝔸}_K^1$  (or $X=K,ℝ,ℂ$ 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.