Non-reducedness of the Hilbert schemes of few points

Michał Szachniewicz

Non-reducedness of the Hilbert schemes of few points

Algebraic Geometry 2021-09-27 v1

Authors: Michał Szachniewicz

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.

Keywords

hilbert scheme non-reducedness bialynicki-birula decomposition apolarity obstruction theory points on affine space

Cite

@article{arxiv.2109.11805,
  title  = {Non-reducedness of the Hilbert schemes of few points},
  author = {Michał Szachniewicz},
  journal= {arXiv preprint arXiv:2109.11805},
  year   = {2021}
}

Comments

36 pages

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