Date: Wednesday, October 20, 2021
Location: 4096 East Hall (4:00 PM to 5:30 PM)
Title: Elliptic quintics on cubic fourfolds, moduli spaces of O'Grady 10 type, and intermediate Jacobian fibration
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 \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 fiberation 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 Laura Pertusi.
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Speaker: Xiaolei Zhao
Institution: UC Santa Barbara
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