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Multi-Harnack smoothings of real plane branches

Pedro Daniel González PérezJean-Jacques Risler — 2010

Annales scientifiques de l'École Normale Supérieure

Let Δ 𝐑 2 be an integral convex polygon. G. Mikhalkin introduced the notion of, a class of real algebraic curves, defined by polynomials supported on Δ and contained in the corresponding toric surface. He proved their existence, viamethod, and that the topological type of their real parts is unique (and determined by Δ ). This paper is concerned with the description of the analogous statement in the case of a smoothing of a real plane branch ( C , 0 ) . We introduce the class ofsmoothings of ( C , 0 ) by passing through...

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