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Gushel-Mukai varieties
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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.
Forward citations
Cited by 2 Pith papers
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Infinitesimal Torelli problems for special Gushel-Mukai and related Fano threefolds: Hodge theoretical and categorical perspectives
For special Gushel-Mukai threefolds, the invariant part of the infinitesimal period map is injective, and the kernel of the full period map has dimension exactly three.
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A rationality criterion for real Fano threefolds
For smooth geometrically rational real Fano threefolds with nonempty real locus, the absence of any deformation-equivalent real form with disconnected real locus forces R-rationality.
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