Singularity which has no M-smoothing.

Viatcheslav Kharlamov (1) , Stepan Orevkov , Eugenii Shustin

1 IRMA - Institut de Recherche Mathématique Avancée

The Harnack bound on the number of real components of a plane real algebraic curve has a natural local version which states that the number of closed real components obtained by a perturbation of a real isolated plane curve singularity having at least one real branch is bounded by the genus of the singularity (perturbations providing this extremal value are called M-smoothings). We show that the latter bound is not sharp for some, explicitly given, singularity.

Mots clés: real singular points; real ovals; "real singular points; Harnack bound; real ovals"

Domaines: Variables complexes [math.CV]

Viatcheslav Kharlamov, Stepan Orevkov, Eugenii Shustin. Singularity which has no M-smoothing.. 1998. ⟨hal-00129575⟩