Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 4 min ago
PreprintCC BY 4.0arXiv

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

  • Fatemeh Rezaee
  • Parsa Saberi
Open at sourcePDFDOICite

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 Briançon-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.

Related

  1. A vanishing-cycle obstruction to smoothing Calabi-Yau threefolds
    Bernd Johannes Wuebben
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. A Novel Steganography Scheme Using Quantum Hilbert Transform
    Nitin Jha, Abhishek Parakh
    arXivPreprintCC BY 4.0Full textGeneral mathematicsQuantum physics & quantum informationarXiv
  3. A sphere obstruction for the Hilbert shift quotient
    Avik Das, Christian Rosendal
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Irrational components of the Hilbert scheme of points
    Gavril Farkas, Rahul Pandharipande, Alessio Sammartano
    Forum of Mathematics, SigmaPeer-reviewedCC BY 4.0Full textGeometry & topologyCrossref
  5. Local monodromy, Behrend function and Hilbert scheme of points on ℂ3
    Yunfeng Jiang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{rezaee2026obstruction,
  title = {{An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds}},
  author = {Fatemeh Rezaee and Parsa Saberi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04054},
  eprint = {2609.04054},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04054},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds
AU  - Fatemeh Rezaee
AU  - Parsa Saberi
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04054
UR  - https://arxiv.org/abs/2609.04054
AB  - 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 Briançon-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.
ER  -