| Résume | The first part of Hilbert's sixteenth problem asks to study the possible arrangements of the connected components of the real part of a real algebraic curve of a given degree in the real projective plane. A useful tool to attack this problem is Viro's combinatorial patchworking method, which allows one to construct real algebraic hypersurfaces starting from a purely combinatorial data : a triangulation with signs on its vertices. All possible arrangements up to degree 7 are realizable using the so-called primitive version of combinatorial patchworking. On the other hand, Itenberg has shown that this is not the case in general, his first counter example being in degree 36. We elaborate on results of B. Haas to prove that already in degree 8, there are some arrangements of connected components that cannot be obtained using primitive combinatorial patchworking. |
