2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58837We study the following question: fix a sufficient general curve D of degree d in P^2, what is the least number of intersections between D and an irreducible curve of degree m? G. Xu proved this number i(d, m) is at least d - 2 for all m. This problem can be regarded as the algebraic part of Kobayashi conjecture on the hyperbolicity of P^2 D. We first improved Xu's bound with m fixed and then generalized his result to rational ruled surfaces.13 pages in AMS-LATEX. To appear on MRLAlgebraic Geometry14H10; 32Q45text