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arXiv · 2503.03390

Infinity Branches and Asymptotic Analysis of Algebraic Space Curves: New Techniques and Applications

Sonia Pérez-Díaz·Li-Yong Shen·Xin-Yu Wang·R. Magdalena-Benedicto
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Abstract

Let C represent an irreducible algebraic space curve defined by the real polynomials fi(x1, x2, x3) for i = 1, 2. It is a recognized fact that a birational relationship invariably exists between the points on C and those on an associated irreducible plane curve, denoted as Cp. In this work, we leverage this established relationship to delineate the asymptotic behavior of C by examining the asymptotes of Cp. Building on this foundation, we introduce a novel and practical algorithm designed to efficiently compute the asymptotes of C, given that the asymptotes of Cp have been ascertained.

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Sonia Pérez-Díaz, Li-Yong Shen, Xin-Yu Wang, R. Magdalena-Benedicto. 2025-03-05. Infinity Branches and Asymptotic Analysis of Algebraic Space Curves: New Techniques and Applications. https://arxiv.org/abs/2503.03390

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