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

2022/10/03 by Yuze Luan, Luan, Yuze · 1 citation
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2210.01170

openalex publication_date 2022/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Stabilization of intersection Betti numbers for moduli spaces of one-dimensional sheaves on surfaces

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