Asymptotic geometry of algebraic curves. (Géométrie asymptotique des courbes algébriques.) (French) Zbl 0949.03064

The purpose of this paper is to apply nonstandard analysis to the study of infinite branches of algebraic curves. If an unlimited point \(M\) of an algebraic curve \(C\) is \(\omega\vec V_1+\omega\vec V_2\), then \(C\) has an asymptotic of direction \(\vec V_1\Leftrightarrow\omega e\) is limited. We can learn the intention from the author’s analysis of the example \(x^3-x^2y+ y^2=0\) by some intuitive properties of infinitesimals.
Reviewer: K.Iséki (Osaka)


03H05 Nonstandard models in mathematics
14H20 Singularities of curves, local rings
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