TL;DR
This survey explores the geometry, moduli, Hodge structures, and categorical properties of Gushel-Mukai varieties, which are special intersections involving Grassmannians, providing a comprehensive overview of their mathematical features.
Contribution
It consolidates recent joint and prior research on Gushel-Mukai varieties, highlighting their geometric and categorical aspects in a unified survey.
Findings
Detailed descriptions of the geometry of Gushel-Mukai varieties
Analysis of their moduli spaces and Hodge structures
Discussion of categorical frameworks related to these varieties
Abstract
Gushel-Mukai varieties are smooth complex dimensionally transverse intersections of a cone over the Grassmannian 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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology