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Irrational components of the Hilbert scheme of points

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arxiv 2405.11997 v2 pith:NT2RR4U7 submitted 2024-05-20 math.AG math.AC

Gavril Farkas , Rahul Pandharipande , Alessio Sammartano This is my paper · ORCID
classification math.AGmath.AC
keywords hilbertcomponentsirrationalpointsschemeirreduciblejelisiejewschemes
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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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Cited by 3 Pith papers

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

  1. The Iarrobino scheme: a self-dual analogue of the Hilbert scheme of points

    math.AG 2025-08 conditional novelty 9.0 of 10

    The Iarrobino scheme compactifying oriented Gorenstein points is constructed for all quasi-projective schemes and is proven smooth over smooth curves, with applications to Hilbert scheme deformation theory and charact...

  2. 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.

  3. A proof of the Brian\c{c}on-Iarrobino Conjecture in three dimensions

    math.AG 2025-08 conditional novelty 7.0 of 10

    For l = binom(k+2,3), the tangent space of Hilb^l(A^3) is maximized uniquely at the monomial ideal m_k, proving the 3D Briancon-Iarrobino Conjecture.

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