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

Yuze Luan

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

Algebraic Geometry 2023-10-24 v2

Authors: Yuze Luan

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.

Keywords

hilbert scheme of points non-reduced curves irreducible components multiplicities partitions

Cite

@article{arxiv.2210.01170,
  title  = {Irreducible components of Hilbert scheme of points on non-reduced curves},
  author = {Yuze Luan},
  journal= {arXiv preprint arXiv:2210.01170},
  year   = {2023}
}

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