28 oct 2020 -- 15:00
DM, Pisa (online)
Seminario di geometria algebrica e aritmetica di Pisa
Abstract.
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 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 M˜ which is a compactification of the twisted intermediate Jacobian of the cubic fourfold. Secondly, we show that 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.