Small elementary components of Hilbert schemes of points
| Autor: | Satriano, Matthew, Staal, Andrew P. |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $2$. |
| Databáze: | arXiv |
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