Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 33 min ago
Peer-reviewedCC BY 4.0Forum of Mathematics, Sigma

Irrational components of the Hilbert scheme of points

  • Gavril Farkas1
  • Rahul Pandharipande2
  • Alessio Sammartano3
  1. 1Humboldt-Universität zu Berlin
  2. 2ETH Zürich
  3. 3Politecnico di Milano
Open at sourcePDFDOICite

Abstract

We construct irrational irreducible components of the Hilbert scheme of points of affine space A n 𝔸n double struck upper A Superscript n for n ≥ 12 n ≥ 12 n greater than or equals 12 . We start with irrational components of the Hilbert scheme of curves in CP 3 ℂℙ3 double struck upper C upper P cubed and use methods developed by Jelisiejew to relate these to irreducible components of the Hilbert schemes of points of A n 𝔸n double struck upper A Superscript n . The result solves Problem XX of the Hilbert scheme of points problem list [J24].

Related

  1. An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds
    Fatemeh Rezaee, Parsa Saberi
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  2. Local monodromy, Behrend function and Hilbert scheme of points on ℂ3
    Yunfeng Jiang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. A Novel Steganography Scheme Using Quantum Hilbert Transform
    Nitin Jha, Abhishek Parakh
    arXivPreprintCC BY 4.0Full textGeneral mathematicsQuantum physics & quantum informationarXiv
  4. Non-reducedness of the Hilbert schemes of few points
    Michał Szachniewicz
    Mathematische ZeitschriftPeer-reviewedLicence not statedFull text15 citedGeometry & topologyOpenAlex
  5. Hochschild cohomology of Hilbert schemes of points on surfaces
    Pieter Belmans, Lie Fu, Andreas Krug
    Journal für die reine und angewandte MathematikPeer-reviewedCC BY 4.0Full textGeometry & topologyHAL

Cite

BibTeXRIS
BibTeX
@article{farkas2026irrational,
  title = {{Irrational components of the Hilbert scheme of points}},
  author = {Gavril Farkas and Rahul Pandharipande and Alessio Sammartano},
  journal = {Forum of Mathematics, Sigma},
  year = {2026},
  month = oct,
  doi = {10.1017/fms.2026.10285},
  url = {https://www.cambridge.org/core/product/identifier/S2050509426102850/type/journal_article},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Irrational components of the Hilbert scheme of points
AU  - Gavril Farkas
AU  - Rahul Pandharipande
AU  - Alessio Sammartano
PY  - 2026
DA  - 2026/10/19
JO  - Forum of Mathematics, Sigma
DO  - 10.1017/fms.2026.10285
UR  - https://www.cambridge.org/core/product/identifier/S2050509426102850/type/journal_article
AB  - We construct irrational irreducible components of the Hilbert scheme of points of affine space A n 𝔸^n double struck upper A Superscript n for n ≥ 12 n ≥ 12 n greater than or equals 12 . We start with irrational components of the Hilbert scheme of curves in CP 3 ℂℙ^3 double struck upper C upper P cubed and use methods developed by Jelisiejew to relate these to irreducible components of the Hilbert schemes of points of A n 𝔸^n double struck upper A Superscript n . The result solves Problem XX of the Hilbert scheme of points problem list [J24].
SN  - 2050-5094
ER  -