2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225664Let $\mathrm{Hilb}^gS$ be the Hilbert scheme of $g$ points on a K3 surface $S$. Suppose that $\mathrm{Pic}S\cong\Z C$ where $C$ is a smooth curve with $C^2=2(g-1)n^2$. We prove that $\mathrm{Hilb}^gS$ is a Lagrangian fibration.21 pages, original (stronger) version of Theorem 2 provedAlgebraic Geometry53C26; 14D06; 14J28; 14J60text