发表机构
Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma（罗马大学古伊多·卡斯特尔努奥沃数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文受Corvaja和Zannier问题启发，研究实环面上三条实代数曲线投影的三重交点，对三条直线给出完整分类，对高次曲线用Siegel和Levin定理得有限性结果，并构造无穷多三重交点的显式例子。
AI 中文摘要
受Corvaja和Zannier一个问题的启发，我们研究三条实平面代数曲线在实环面上的投影是否具有无穷多个三重交点。我们详细分析了三条直线的情形，得到了完整的分类。对于高次曲线，我们利用Siegel和Levin关于曲线上整点的定理推导出若干有限性结果。另一方面，我们构造了具有无穷多个三重交点的高次曲线的显式例子。
英文摘要
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.
Comments28 pages
