Algebraic and Arithmetic Geometry Seminar

Elliptic quintics on cubic fourfolds, O'Grady 10 and Lagrangian fibrations

by Laura Pertusi (Università di Milano Statale)

Google Meet

Google Meet


In this talk we study certain moduli spaces of semistable objects in the Kuznetsov component of a cubic fourfold. We show that they admit a symplectic resolution $\tilde M$ which is a smooth projective hyperkaehler manifold deformation equivalent to the 10-dimensional example constructed by O'Grady. As a first application, we construct a birational model of $\tilde M$ which is a compactification of the twisted intermediate Jacobian of the cubic fourfold. Secondly, we show that $\tilde M$ is the MRC quotient of the main component of the Hilbert scheme of elliptic quintic curves in the cubic fourfold, as conjectured by Castravet. This is a joint work with Chunyi Li and Xiaolei Zhao.