Deformations of the connected sum of Gorenstein algebras
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917267940311040 |
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| author | Oszer, Piotr |
| author_facet | Oszer, Piotr |
| contents | We prove that the Gorenstein locus of the Hilbert scheme of points on $\mathbb A^n$ is non-reduced for $n\geq 12$; we construct examples of non-reduced points that come from apolar algebras of the sum of general cubics. As a corollary, we get a non-reducedness result for the cactus scheme. We generalise the Białynicki-Birula decomposition to abstract deformation functors, providing a new method of studying deformation theory. Our construction gives us fractal structures on the nested Hilbert scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deformations of the connected sum of Gorenstein algebras Oszer, Piotr Algebraic Geometry Commutative Algebra 14B10 (Primary), 13D10, 14D15, 14C05 (Secondary) We prove that the Gorenstein locus of the Hilbert scheme of points on $\mathbb A^n$ is non-reduced for $n\geq 12$; we construct examples of non-reduced points that come from apolar algebras of the sum of general cubics. As a corollary, we get a non-reducedness result for the cactus scheme. We generalise the Białynicki-Birula decomposition to abstract deformation functors, providing a new method of studying deformation theory. Our construction gives us fractal structures on the nested Hilbert scheme. |
| title | Deformations of the connected sum of Gorenstein algebras |
| topic | Algebraic Geometry Commutative Algebra 14B10 (Primary), 13D10, 14D15, 14C05 (Secondary) |
| url | https://arxiv.org/abs/2601.03179 |