Triple intersections for algebraic curves on the real torus

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.