Local Equations for Hilbert Schemes of Points
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917037177044992 |
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| author | Ilten, Nathan Meazzini, Francesco Petracci, Andrea |
| author_facet | Ilten, Nathan Meazzini, Francesco Petracci, Andrea |
| contents | We compute the completion of the local ring of the Hilbert scheme of degree $n+1$ subschemes of $\mathbb{A}^n$ at the point corresponding to the ideal $\langle x_1,\ldots,x_n\rangle^2$, and describe the completion of the universal family. For the purposes of comparison, we do this computation with both classical and DGLA methods. We use our explicit equations to produce high dimensional linear subspaces of the Hilbert scheme, and compare our equations with those coming from deformations of based algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07066 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local Equations for Hilbert Schemes of Points Ilten, Nathan Meazzini, Francesco Petracci, Andrea Algebraic Geometry Commutative Algebra Primary: 14C05, 14B07, Secondary: 14D15, 13E10, 13D10 We compute the completion of the local ring of the Hilbert scheme of degree $n+1$ subschemes of $\mathbb{A}^n$ at the point corresponding to the ideal $\langle x_1,\ldots,x_n\rangle^2$, and describe the completion of the universal family. For the purposes of comparison, we do this computation with both classical and DGLA methods. We use our explicit equations to produce high dimensional linear subspaces of the Hilbert scheme, and compare our equations with those coming from deformations of based algebras. |
| title | Local Equations for Hilbert Schemes of Points |
| topic | Algebraic Geometry Commutative Algebra Primary: 14C05, 14B07, Secondary: 14D15, 13E10, 13D10 |
| url | https://arxiv.org/abs/2510.07066 |