On the representability of ${\Cal Hilb}^nk[x]_{(x)}$

Roy M. Skjelnes

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arXiv · math/9912138

On the representability of ${\Cal Hilb}^nk[x]_{(x)}$

Roy M. Skjelnes

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Abstract

Let $k[x]_{(x)}$ be the polynomial ring $k[x]$ localized in the maximal ideal $(x)\subseteq k[x]$. We study the Hilbert functor parameterizing ideals of colength $n$ in this ring {\it having support at the origin}. The main result of this article is that this functor is not representable. We also give a complete description of the functor as a limit of representable functors.

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Roy M. Skjelnes. 1999-12-17. On the representability of ${\Cal Hilb}^nk[x]_{(x)}$. https://arxiv.org/abs/math/9912138

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