Gushel-Mukai varieties


Gushel-Mukai varieties are dimensionally transverse intersections of a cone over Grassmannian Gr(2,5) with a quadric. They include all mildly singular Fano varieties with Picard number 1, coindex 3, and degree 10. I will discuss the geometry of this class of varieties (including their birational properties and the structure of their derived categories) and their relation to Eisenbud-Popescu-Walter sextics. This material is covered by joint works with Olivier Debarre and Alex Perry.