An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds

Fatemeh Rezaee; Parsa Saberi

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arXiv · 2609.04054

An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds

Fatemeh Rezaee·Parsa Saberi

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Abstract

We prove a necessary condition conjecture ([27, Conjecture B]) for the maximal singularity of the Hilbert scheme of points in 3D for a large class of degrees, which in particular implies the 1978 Brian\c{c}on-Iarrobino Conjecture for a tetrahedral degree, and vastly generalises the result in [19]. The novelty lies in introducing a new upper bound on the dimensions of the tangent spaces of the claimed non-maximally singular ideals, constructing canonical ideals that satisfy the claimed maximal singularity condition, providing a lower bound on the dimension of their tangent spaces, and finally comparing the two cases.

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BibTeX RIS

Fatemeh Rezaee, Parsa Saberi. 2026-09-03. An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds. https://arxiv.org/abs/2609.04054

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