In this talk, we relate the defect σ(X) := b4(X) − b2(X) of a singular cubic threefold X to various geometric properties of X. The question is motivated by the construction of the exceptional example of a Hyperkähler manifold of type O’Grady 10 from a cubic fourfold by Laza, Saccà and Voisin. By a result of Brosnan, the defect of hyperplane sections of the cubic fourfold is an obstruction for the LSV construction to work. The talk is based on a joint work in progress with Lisa Marquand.
This video was produced by the Hausdorff Center for Mathematics as part of the workshop K3 surfaces, hyperkähler manifolds, and cubic fourfolds.
