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arXiv · 2112.01481

Small elementary components of Hilbert schemes of points

Matthew Satriano·Andrew P. Staal
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Abstract

We answer an open problem posed by Iarrobino in the '80s: is there an elementary component of the Hilbert scheme of points $\textrm{Hilb}^d(\mathbb{A}^n)$ with dimension less than $(n-1)(d-1)$? We construct an infinite class of such components in $\textrm{Hilb}^d(\mathbb{A}^4)$. Our techniques also allow us to construct an explicit example of a local Artinian ring with trivial negative tangents, vanishing nonnegative obstruction space, and socle-dimension $2$.

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Matthew Satriano, Andrew P. Staal. 2021-12-02. Small elementary components of Hilbert schemes of points. https://arxiv.org/abs/2112.01481

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