Gushel–Mukai varieties: Linear spaces and periods

By O. Debarre, Alexander Kuznetsov. Kyoto Journal of Mathematics, 2016

55 citations recorded by the source corpus.

Beauville and Donagi proved in 1985 that the primitive middle cohomology of a smooth complex cubic fourfold and the primitive second cohomology of its variety of lines, a smooth hyperk\"ahler fourfold, are isomorphic as polarized integral Hodge structures. We prove analogous statements for smooth complex Gushel-Mukai varieties of dimension 4 (resp. 6), i.e., smooth dimensionally transverse intersections of the cone over the Grassmannian Gr(2,5), a quadric, and two hyperplanes (resp. of the cone over Gr(2,5) and a quadric). The associated hyperk\"ahler fourfold is in both cases a smooth double cover of a hypersurface in ${\bf P}^5$ called an EPW sextic.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/740d6ef0219105bc4e8c559a02c8ca15176643b4