Irrational components of the Hilbert scheme of points
Abstract
We construct irrational irreducible components of the Hilbert scheme of points of affine n-dimensional space, for n at least 12. We start with irrational components of the Hilbert scheme of curves in P3 and use methods developed by Jelisiejew to relate these to irreducible components of the Hilbert schemes of points of An. The result solves Problem XX of [J. Jelisiejew, Open problems in deformations of Artinian algebras, Hilbert schemes and around, arXiv:2307.08777, 2023].
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