A proof of the Briançon-Iarrobino Conjecture in three dimensions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915470401077248 |
|---|---|
| author | Mackenzie, Owen Rezaee, Fatemeh |
| author_facet | Mackenzie, Owen Rezaee, Fatemeh |
| contents | We resolve the 1978 Briançon-Iarrobino Conjecture regarding the maximum singularity of $\mathcal{H}=\mathrm{Hilb}^{l}(\mathbb{A}^3)$, where $l$ is a tetrahedral number, by refining the work of Ramkumar-Sammartano in \cite{Ramkumar-Sammartano}. This also immediately implies the conjectural necessary condition for a point of $\mathcal{H}$ to have the maximal singularity, suggested by the second-named author in \cite{Rezaee-23-Conjectures}. In a sequel to this article, \cite{Mackenzie-Rezaee2}, we prove a generalized version of this conjecture for certain non-tetrahedral $l$, via proving the conjectural necessary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A proof of the Briançon-Iarrobino Conjecture in three dimensions Mackenzie, Owen Rezaee, Fatemeh Algebraic Geometry Commutative Algebra Combinatorics Representation Theory We resolve the 1978 Briançon-Iarrobino Conjecture regarding the maximum singularity of $\mathcal{H}=\mathrm{Hilb}^{l}(\mathbb{A}^3)$, where $l$ is a tetrahedral number, by refining the work of Ramkumar-Sammartano in \cite{Ramkumar-Sammartano}. This also immediately implies the conjectural necessary condition for a point of $\mathcal{H}$ to have the maximal singularity, suggested by the second-named author in \cite{Rezaee-23-Conjectures}. In a sequel to this article, \cite{Mackenzie-Rezaee2}, we prove a generalized version of this conjecture for certain non-tetrahedral $l$, via proving the conjectural necessary condition. |
| title | A proof of the Briançon-Iarrobino Conjecture in three dimensions |
| topic | Algebraic Geometry Commutative Algebra Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2508.21717 |