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

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.
Gianni, Patrizia
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/6825
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