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

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

1999-12-17

arxiv.org/abs/math/9912138v1

Mathematics

Algebraic Geometry

Scientific paper

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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