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arXiv · 2109.11805

Non-reducedness of the Hilbert schemes of few points

Michał Szachniewicz
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Abstract

We use generalised Bialynicki-Birula decomposition, apolarity and obstruction theories to prove non-reducedness of the Hilbert scheme of $13$ points on $\mathbb{A}^6$. Our argument doesn't involve computer calculations and gives an example of a fractal-like structure on this Hilbert scheme.

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Michał Szachniewicz. 2021-09-24. Non-reducedness of the Hilbert schemes of few points. https://arxiv.org/abs/2109.11805

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