Mathematics

I will discuss the structure of derived categories of Fano manifolds of degree 10. They admit a semiorthogonal decomposition with several exceptional objects (coming from the ambient Grassmannian) and a nontrivial component, which in the case of even dimension behaves like derived category of a K3 surface. Conjecturally, the varieties related by the correspondence of the previous talk have equivalent nontrivial components. I will prove this in some cases. This is a work in progress joint with Alex Perry.