May 16, Wednesday, 15:30, room 211

Andrei Konovalov

Quadric hypersurfaces, Grassmannians and triality

The set of k-dimensional linear subspaces of a smooth complex quadric hypersurface of dimension 2k is a subvariety of Gr(k+1,2k+2). Like in the classical case of two-dimensional quadric, this variety splits into two irreducible components. In my talk, I will use Schubert calculus to prove the “triality” property of six-dimensional quadric: variety of 3-planes in this quadric is a disjoint union of two components and each of them is isomorphic to the original quadric.