Forcing equation/Line/Example

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.