Rocky Mountain Journal of Mathematics

Some elementary components of the Hilbert scheme of points

Mark E. Huibregtse

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Abstract

Let $K$ be an algebraically closed field of characteristic~$0$, and let $H^{\mu }_{\mathbb {A}^n_{K }}$ denote the Hilbert scheme of $\mu $ points of $\mathbb {A}^n_{K}$. An \textit {elementary component} $E$ of $H^{\mu }_{\mathbb {A}^n_{K }}$ is an irreducible component such that every $K$-point $[I]\in E$ represents a length-$\mu $ closed subscheme $Spec (K [x_1,\ldots ,x_n]/I)\subseteq \mathbb {A}^n_{K}$ that is supported at one point. Iarrobino and Emsalem gave the first explicit examples (with $\mu > 1$) of elementary components \cite {Iarrob-Emsalem}; in their examples, the ideals $I$ were homogeneous (up to a change of coordinates corresponding to a translation of $\mathbb {A}^n_{K}$). We generalize their construction to obtain new examples of elementary components.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 4 (2017), 1169-1225.

Dates
First available in Project Euclid: 6 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1501984946

Digital Object Identifier
doi:10.1216/RMJ-2017-47-4-1169

Mathematical Reviews number (MathSciNet)
MR3689951

Zentralblatt MATH identifier
06790011

Subjects
Primary: 14C05: Parametrization (Chow and Hilbert schemes)

Keywords
Generic algebra small tangent space Hilbert scheme of points elementary component

Citation

Huibregtse, Mark E. Some elementary components of the Hilbert scheme of points. Rocky Mountain J. Math. 47 (2017), no. 4, 1169--1225. doi:10.1216/RMJ-2017-47-4-1169. https://projecteuclid.org/euclid.rmjm/1501984946


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