2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73431We prove the "strong form" of the Clemens conjecture in degree 10. Namely, on a general quintic threefold F in P^4, there are only finitely many smooth rational curves of degree 10, and each curve is embedded in F with normal bundle O(-1)^2. Moreover, in degree 10, there are no singular, reduced, and irreducible rational curves, nor any reduced, reducible, and connected curves with rational components in F.The justification of Fact 1 on p. 10 has been made clearer; minor formatting issues and typos corrected. To appear in Communications in AlgebraAlgebraic Geometry14J30; 13P10, 14H45text