 "Hilbert scheme" sometimes refers to the punctual Hilbert scheme of 0-dimensional subschemes on a scheme.Informally this can be thought of as something like finite collections of points on a scheme, though this picture can be very misleading when several points coincide.There is a Hilbert–Chow morphism from the reduced Hilbert scheme of points to the Chow variety of cycles taking any 0-dimensional scheme to its associated 0-cycle.