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Peer-reviewedCC BYEMS Surveys in Mathematical Sciences

Gushel–Mukai varieties

  • Olivier Debarre1
  1. 1Université Paris Cité, France
Open at sourceDOICite

Abstract

Gushel–Mukai varieties are smooth complex dimensionally transverse intersections of a cone over the Grassmannian \mathsf{Gr}(2,5) with a linear space and a quadratic hypersurface. The aim of this survey is to discuss the geometry, moduli, Hodge structures, and categorical aspects of these varieties. It is based on joint work with Alexander Kuznetsov and earlier work of Logachev, Iliev, Manivel, O’Grady, and others.

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Cite

BibTeXRIS
BibTeX
@article{debarre2026gushelmukai,
  title = {{Gushel–Mukai varieties}},
  author = {Olivier Debarre},
  journal = {EMS Surveys in Mathematical Sciences},
  year = {2026},
  month = nov,
  doi = {10.4171/emss/125},
  url = {https://doi.org/10.4171/emss/125},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Gushel–Mukai varieties
AU  - Olivier Debarre
PY  - 2026
DA  - 2026/11/06
JO  - EMS Surveys in Mathematical Sciences
DO  - 10.4171/emss/125
UR  - https://doi.org/10.4171/emss/125
AB  - Gushel–Mukai varieties are smooth complex dimensionally transverse intersections of a cone over the Grassmannian \mathsf{Gr}(2,5) with a linear space and a quadratic hypersurface. The aim of this survey is to discuss the geometry, moduli, Hodge structures, and categorical aspects of these varieties. It is based on joint work with Alexander Kuznetsov and earlier work of Logachev, Iliev, Manivel, O’Grady, and others.
SN  - 2308-2151
SN  - 2308-216X
ER  -