PreprintCC BY 4.0arXiv
Triple intersections for algebraic curves on the real torus
Abstract
Motivated by a question of Corvaja and Zannier, we investigate whether the projections on the real torus of three real algebraic plane curves admit infinitely many triple intersections. We analyze the case of three lines in detail, obtaining a complete classification. For higher-degree curves, we derive several finiteness results using Siegel's and Levin's theorems on integral points on curves. On the other hand, we construct explicit examples of higher-degree curves with infinitely many triple intersections.
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BibTeX
@misc{avaro2026triple,
title = {{Triple intersections for algebraic curves on the real torus}},
author = {Danilo Avaro},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09231},
eprint = {2609.09231},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09231},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Triple intersections for algebraic curves on the real torus
AU - Danilo Avaro
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.09231
UR - https://arxiv.org/abs/2609.09231
AB - Motivated by a question of Corvaja and Zannier, we investigate whether the projections on the real torus of three real algebraic plane curves admit infinitely many triple intersections. We analyze the case of three lines in detail, obtaining a complete classification. For higher-degree curves, we derive several finiteness results using Siegel's and Levin's theorems on integral points on curves. On the other hand, we construct explicit examples of higher-degree curves with infinitely many triple intersections.
ER -