More elementary components of the Hilbert scheme of points

2021/01/31 by Mark E. Huibregtse, Huibregtse, Mark E. · 1 citation
Mathematics · #14C05 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2102.00494

openalex publication_date 2021/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be an algebraically closed field of characteristic 0, and let H^μ denote the Hilbert scheme of μ points of the affine space Aⁿ. An elementary component E of H^μ is an irreducible component such that every K-point [I] ∈ E represents a length-μ closed subscheme Spec(K[x₁,…,x_n]/I) ⊆ Aⁿ that is supported at one point. In a previous article we found some new examples of elementary components; in this article, we simplify the methods and extend the range of the previous paper to find several more examples. In addition, we present a "plausibility test" that suggests the existence of a vast number of similar examples.

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