Irreducible components of Hilbert scheme of points on non-reduced curves
Yuze Luan
Journal of Singularities
volume 29 (2026), 199-216
Received: 16 August 2025. In revised form: 6 February 2026
Abstract:
We classify the irreducible components of the Hilbert scheme of n points on non-reduced algebraic plane curves, and give a formula for the multiplicities of the irreducible components. The irreducible components 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.
Author(s) information:
Yuze Luan