The Hilbert's sexteenth problem, consisting in the determination of the topology of real algebraic curves, is totally solved for the curves of degree m, m≤7. For higer degrees, many inequalities have been proved in order to give bounds of the number of admissible configurations: among them the Arnold-Wilson's inequalities. In this paper we recall the main results and we prove that two Arnold-Wilson's inequalities are sharp. Examples are constructed of real algebraic curves for which the bounds are reached.
|Autori interni:||GIANNI, PATRIZIA|
|Titolo:||Sulle diseguaglianze di Arnold-Wilson per le curve algebriche reali|
|Anno del prodotto:||1982|
|Digital Object Identifier (DOI):||10.1007/BF02900759|
|Appare nelle tipologie:||1.1 Articolo in rivista|