Gushel–Mukai varieties

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.