Maximal smoothings of real plane curve singular points.
Kharlamov, Viatcheslav ; Risler, Jean-Jacques ; Shustin, Eugenii
HAL, hal-00129577 / Harvested from HAL
Text on HAL
The local Harnack inequality bounds from above the number of ovals which can appear in a small perturbation of a singular point. As is known, there are singular points for which this bound is not sharp. We show that Harnack inequality is sharp in any complex topologically equisingular class: every real plane curve singular point is complex deformation equivalent to a real singularity for which Harnack inequality is sharp. For semi-quasi-homogeneous and some other singularities we exhibit a real deformation with the same property. A refined Harnack inequality and its sharpness are discussed also.
Publié le : 1998-07-05
Classification:  real singularities,  equisingular deformations,  "real singularities,  Harnack bound,  equisingular deformations",  32S50, 14P99,32S15,  [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] 
@article{hal-00129577,
     author = {Kharlamov, Viatcheslav and Risler, Jean-Jacques and Shustin, Eugenii},
     title = {Maximal smoothings of real plane curve singular points.},
     journal = {HAL},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00129577}
}

Kharlamov, Viatcheslav; Risler, Jean-Jacques; Shustin, Eugenii. Maximal smoothings of real plane curve singular points.. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129577/