  We construct solutions of the fast diffusion equation, which exist for all
$t\in\mathbb{R}$ and are singular on the set $\Gamma(t):= \{ \xi(s) ; -\infty
<s \leq ct \}$, $c>0$, where $\xi\in C^3(\mathbb{R};\mathbb{R}^n)$, $n\geq 2$.
We also give a precise description of the behavior of the solutions near
$\Gamma(t)$.
