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arXiv · 2601.03179

Deformations of the connected sum of Gorenstein algebras

Piotr Oszer
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Abstract

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 Bia{\l}ynicki-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.

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Piotr Oszer. 2026-01-06. Deformations of the connected sum of Gorenstein algebras. https://arxiv.org/abs/2601.03179

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