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arXiv · 2405.11997

Irrational components of the Hilbert scheme of points

Gavril Farkas·Rahul Pandharipande·Alessio Sammartano
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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 P^3 and use methods developed by Jelisiejew to relate these to irreducible components of the Hilbert schemes of points of A^n. 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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Gavril Farkas, Rahul Pandharipande, Alessio Sammartano. 2024-05-20. Irrational components of the Hilbert scheme of points. https://arxiv.org/abs/2405.11997

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