Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 59, Number 4 (2019), 897-953.
Gushel–Mukai varieties: Linear spaces and periods
Beauville and Donagi proved in 1985 that the primitive middle cohomology of a smooth complex cubic -fold and the primitive second cohomology of its variety of lines, a smooth hyper-Kähler -fold, are isomorphic as polarized integral Hodge structures. We prove analogous statements for smooth complex Gushel–Mukai varieties of dimension (resp., ), that is, smooth dimensionally transverse intersections of the cone over the Grassmannian , a quadric, and two hyperplanes (resp., of the cone over and a quadric). The associated hyper-Kähler -fold is in both cases a smooth double cover of a hypersurface in called an Eisenbud–Popescu–Walter sextic.
Kyoto J. Math., Volume 59, Number 4 (2019), 897-953.
Received: 3 February 2017
Revised: 6 June 2017
Accepted: 20 June 2017
First available in Project Euclid: 26 September 2019
Permanent link to this document
Digital Object Identifier
Primary: 14D07: Variation of Hodge structures [See also 32G20]
Secondary: 14J35: $4$-folds 14J40: $n$-folds ($n > 4$) 14J45: Fano varieties 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 32G20: Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]
Debarre, Olivier; Kuznetsov, Alexander. Gushel–Mukai varieties: Linear spaces and periods. Kyoto J. Math. 59 (2019), no. 4, 897--953. doi:10.1215/21562261-2019-0030. https://projecteuclid.org/euclid.kjm/1569484830