Irreducible components of Hilbert scheme of points on non-reduced curves, preprint.

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.

https://arxiv.org/pdf/2210.01170

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