Tools for analyzing the intersection curve between a torus and a quadric through projection and lifting
Algebraic Geometry
2025-03-13 v1
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 -axis. The paper primarily focuses on examining the curve's projection onto the plane , 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.
Cite
@article{arxiv.2503.08924,
title = {Tools for analyzing the intersection curve between a torus and a quadric through projection and lifting},
author = {Laureano Gonzalez-Vega and Jorge Caravantes and Gema M. Diaz-Toca and Mario Fioravanti},
journal= {arXiv preprint arXiv:2503.08924},
year = {2025}
}