  The configuration space of $n$ marked points on the complex plane is
considered. We investigate a decomposition of this space by so-called
Gauss-skizze i.e. a class of graphs being forests, introduced by Gauss. It is
proved that this decomposition is a semi-algebraic topological stratification.
It also forms a cell decomposition of the configuration space of $n$ marked
points. Moreover, we prove that classical tools from deformation theory, ruled
by a Maurer--Cartan equation, can be used only locally for Gauss-skizze. We
prove that the deformation of the Gauss-skizze is governed by a
Hamilton--Jacobi differential equation. This gives developments concerning
Saito's Frobenius manifold. Finally, a Gauss-skizze operad is introduced. It is
an enriched Fulton--MacPherson operad, topologically equivalent to the little
2-disc operad.
