Gushel-Mukai varieties

Olivier Debarre

Gushel-Mukai varieties

Algebraic Geometry 2025-07-02 v2

Authors: Olivier Debarre

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.

Keywords

fourier-mukai transform grassmannian varieties

Cite

@article{arxiv.2001.03485,
  title  = {Gushel-Mukai varieties},
  author = {Olivier Debarre},
  journal= {arXiv preprint arXiv:2001.03485},
  year   = {2025}
}

Comments

26 pages. Survey article. Typos corrected and a few updates added

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