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.
Sulle diseguaglianze di Arnold-Wilson per le curve algebriche reali
GIANNI, PATRIZIA
1982-01-01
Abstract
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.File in questo prodotto:
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