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arXiv · 2503.08924

Tools for analyzing the intersection curve between a torus and a quadric through projection and lifting

Laureano Gonzalez-Vega·Jorge Caravantes·Gema M. Diaz-Toca·Mario Fioravanti
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Abstract

This article introduces efficient and user-friendly tools for analyzing the intersection curve between a ringed torus and an irreducible quadric surface. Without loose of generality, it is assumed that the torus is centered at the origin, and its axis of revolution coincides with the $z$-axis. The paper primarily focuses on examining the curve's projection onto the plane $z=0$, referred to as the cutcurve, which is essential for ensuring accurate lifting procedures. Additionally, we provide a detailed characterization of the singularities in both the projection and the intersection curve, as well as the existence of double tangents. A key tool for the analysis is the theory of resultant and subresultant polynomials.

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Laureano Gonzalez-Vega, Jorge Caravantes, Gema M. Diaz-Toca, Mario Fioravanti. 2025-03-11. Tools for analyzing the intersection curve between a torus and a quadric through projection and lifting. https://arxiv.org/abs/2503.08924

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