RT Journal Article
T1 Multi-Harnack smoothings of real plane branches
A1 González Pérez, Pedro Daniel
A1 Risler, Jean-Jacques
AB This paper is motivated by the results of G. Mikhalkin about a certain class of real algebraic curves, called Harnack curves, in toric surfaces. Mikhalkin has proved the existence of such curves as well as topological uniqueness of their real locus.The authors are concerned about an analogous statement in the case of a smoothing of a real plane branch (C, 0) _ (C2, 0) (an analytically irreducible germ of a real curve). They introduce the class of multi-Harnack smoothings of (C, 0) and prove its existence along with its topological uniqueness.Theorem 9.3. Any real plane branch (C, 0) has a multi-Harnack smoothing.Theorem 9.4. Let (C, 0) be a real branch. The topological type of multi-Harnack smoothings of (C, 0) is unique. There are at most two signed topological types of multi-Harnack smoothings of (C, 0). These types depend only on the sequence {(nj ,mj)}, which determines and is determined by the embedded topological type of (C, 0) _ (C2, 0). In terms of the parameters, multi-Harnack smoothings are multi-semi-quasi-homogeneous, which lets the authors analyze also the asymptotic multi-scales of the ovals.
PB Société Mathématique de France
SN 0012-9593
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/41939
UL https://hdl.handle.net/20.500.14352/41939
LA eng
NO Ministerio de Educación y Ciencia (MEC)
DS Docta Complutense
RD 6 abr 2025