2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72715We study completely the Hilbert scheme and punctual Hilbert scheme of a nodal curve, and the relative Hilbert scheme of a family of curves acquiring a node. The results are then extended, less completely, to flag Hilbert schemes, parametrizing chains of subschemes. We find, notably, that if the total space $X$ of a family $X/B$ is smooth (over an algebraically closed field $\k$), then the relative Hilbert scheme $Hilb_m(X/B)$ is smooth over $\k$ and the flag Hilbert schemes are normal and locally complete intersection, but generally singular.16 pages, 1 figureAlgebraic Geometry14C05text