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Non-reducedness of the Hilbert schemes of few points

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arxiv 2109.11805 v1 pith:EK2CG4LK submitted 2021-09-24 math.AG

Micha{l} Szachniewicz This is my paper · ORCID
classification math.AG
keywords hilbertnon-reducednesspointsschemeapolarityargumentbialynicki-birulacalculations
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. New components of Hilbert schemes of points and 2-step ideals

    math.AG 2025-07 conditional novelty 8.0 of 10

    2-step ideals provide a new framework for finding reducible Hilbert schemes and elementary components, producing 215 new examples in dimensions 4, 5 and 6.

  2. Degenerations of multisingularities and Artin algebras

    math.AG 2026-07 conditional novelty 7.0 of 10

    A singularity-theoretic 'stable hierarchy' on Artin algebras is shown to be computable from automorphism-group data and to extend the classical degeneration order beyond fixed rank.

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