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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.08924 |
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| _version_ | 1866916650307026944 |
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| author | Gonzalez-Vega, Laureano Caravantes, Jorge Diaz-Toca, Gema M. Fioravanti, Mario |
| author_facet | Gonzalez-Vega, Laureano Caravantes, Jorge Diaz-Toca, Gema M. Fioravanti, Mario |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tools for analyzing the intersection curve between a torus and a quadric through projection and lifting Gonzalez-Vega, Laureano Caravantes, Jorge Diaz-Toca, Gema M. Fioravanti, Mario Algebraic Geometry 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. |
| title | Tools for analyzing the intersection curve between a torus and a quadric through projection and lifting |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2503.08924 |