Algebraic Geometry Seminar
An ordinary Gushel-Mukai fourfold X is a smooth quadric section of a linear section of the Grassmannian G(2,5). Kuznetsov and Perry proved that the bounded derived category of X admits a semiorthogonal decomposition whose non-trivial component is a subcategory of K3 type. In this talk I will report on a joint work with Alex Perry and Laura Pertusi, in which we construct Bridgeland stability conditions on the K3 subcategory of X. Then I will explain some applications concerning the existence of a homological associated K3 surface and related algebraic constructions in hyperkaehler geometry.