| Résume | Denote a (possibly non-reduced, singular) plane curve by C. The irreducible components of the Hilbert scheme of n points on C are indexed by partitions of n; all have dimension n; and their multiplicities are given as a polynomial of the parts of the corresponding partitions. We also classify the irreducible components of the n, n + 1 nest Hilbert scheme of points on the curve C. All the components have the same dimension n + 1 and are indexed by partitions of n satisfying specific combinatorial conditions. |
