Irreducible components of Hilbert scheme of points on non-reduced curves

Yuze Luan

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arXiv · 2210.01170

Irreducible components of Hilbert scheme of points on non-reduced curves

Yuze Luan

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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.

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Yuze Luan. 2022-10-03. Irreducible components of Hilbert scheme of points on non-reduced curves. https://arxiv.org/abs/2210.01170

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