The Defect of a Cubic Threefold

Explore the relationship between the defect σ(X) of a singular cubic threefold X and its geometric properties in this 31-minute lecture from the Hausdorff Center for Mathematics. Delve into the motivation behind this question, stemming from the construction of an exceptional Hyperkähler manifold of type O'Grady 10 from a cubic fourfold by Laza, Saccà, and Voisin. Learn about Brosnan's result, which identifies the defect of hyperplane sections of the cubic fourfold as an obstruction to the LSV construction. Gain insights from the ongoing joint work with Lisa Marquand, as the speaker presents their findings on this intriguing mathematical topic.