EMS Surveys in Mathematical Sciences· 2026Q1· Review
Gushel–Mukai varieties
- 18citations
- Q1SCImago
- 2026year
Short summary
This survey introduces Gushel–Mukai varieties, defined as specific intersections within a cone over the Grassmannian Gr(2,5), a linear space, and a quadratic hypersurface.
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Key points
- Gushel–Mukai varieties are defined as transverse intersections within a cone over Gr(2,5).
- These intersections involve a linear space and a quadratic hypersurface.
- The survey covers their geometry, moduli, Hodge structures, and categorical aspects.
- The work builds on contributions from Logachev, Iliev, Manivel, O’Grady, and others, as well as joint work with Alexander Kuznetsov.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. EMS Surveys in Mathematical Sciences, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics