English

Irrational components of the Hilbert scheme of points

Algebraic Geometry 2024-06-03 v2 Commutative Algebra

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].

Keywords

Cite

@article{arxiv.2405.11997,
  title  = {Irrational components of the Hilbert scheme of points},
  author = {Gavril Farkas and Rahul Pandharipande and Alessio Sammartano},
  journal= {arXiv preprint arXiv:2405.11997},
  year   = {2024}
}