Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 9 min ago
PreprintarXiv licencearXiv

Disconnectedness of the Hilbert Schemes of E6/P6

  • Minyoung Jeon
Open at sourcePDFDOICite

Abstract

In this note, we show that the Hilbert scheme HilbPd,4(t)(E6/P6) associated with the Hilbert polynomial Pd,4(t) is disconnected by determining that it has exactly two connected components. This result adapts Seong's methods, successfully extending the disconnectedness of Grassmannians to the exceptional type E6.

Related

  1. Non-reducedness of the Hilbert schemes of few points
    Michał Szachniewicz
    Mathematische ZeitschriftPeer-reviewedLicence not statedFull text16 citedGeometry & topologyOpenAlex
  2. 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
  3. Stability conditions on products of curves and Hilbert schemes of surfaces
    Chunyi Li, Emanuele Macrì, Alexander Perry +2
    Geometry & TopologyPeer-reviewedCC BYFull text14 citedGeometry & topologyOpenAlex
  4. Nef Cones of Hilbert Schemes of Orthogonal Grassmannians
    Minyoung Jeon
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  5. Hilbert schemes of low-degree rational curves on a prime Fano threefold of degree $22$
    Kiryong Chung, Dae-Won Lee
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{jeon2026disconnectedness,
  title = {{Disconnectedness of the Hilbert Schemes of $E_6/P_6$}},
  author = {Minyoung Jeon},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.06541},
  eprint = {2609.06541},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06541},
}
RIS
TY  - UNPB
TI  - Disconnectedness of the Hilbert Schemes of E_6/P_6
AU  - Minyoung Jeon
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.06541
UR  - https://arxiv.org/abs/2609.06541
AB  - In this note, we show that the Hilbert scheme Hilb_P_d,4(t)(E_6/P_6) associated with the Hilbert polynomial P_d,4(t) is disconnected by determining that it has exactly two connected components. This result adapts Seong's methods, successfully extending the disconnectedness of Grassmannians to the exceptional type E_6.
ER  -