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2017 Some elementary components of the Hilbert scheme of points
Mark E. Huibregtse
Rocky Mountain J. Math. 47(4): 1169-1225 (2017). DOI: 10.1216/RMJ-2017-47-4-1169

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.

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Mark E. Huibregtse. "Some elementary components of the Hilbert scheme of points." Rocky Mountain J. Math. 47 (4) 1169 - 1225, 2017. https://doi.org/10.1216/RMJ-2017-47-4-1169

Information

Published: 2017
First available in Project Euclid: 6 August 2017

zbMATH: 06790011
MathSciNet: MR3689951
Digital Object Identifier: 10.1216/RMJ-2017-47-4-1169

Subjects:
Primary: 14C05

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 4 • 2017
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