For a smooth cubic fourfold Y , we study the moduli space M of semistable objects of Mukai vector 2λ1 + 2λ2 in the Kuznetsov component of Y . We show that with a certain choice of stability conditions, M admits a symplectic resolution ̃M , which is a smooth projective hyperk ̈ahler manifold, deformation equivalent to the 10-dimensional ex- amples constructed by O’Grady. As applications, we show that a birational model of ̃M provides a hyperk ̈ahler compactification of the twisted family of intermediate Jacobians as- sociated to Y . This generalizes the previous result of Voisin [Voi18] in the very general case. We also prove that ̃M is the MRC quotient of the main component of the Hilbert scheme of quintic elliptic curves in Y , confirming a conjecture of Castravet.

Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations / C. Li, L. Pertusi, X. Zhao. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 408:(2022), pp. 108584.1-108584.44. [Epub ahead of print] [10.1016/j.aim.2022.108584]

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

#### Abstract

For a smooth cubic fourfold Y , we study the moduli space M of semistable objects of Mukai vector 2λ1 + 2λ2 in the Kuznetsov component of Y . We show that with a certain choice of stability conditions, M admits a symplectic resolution ̃M , which is a smooth projective hyperk ̈ahler manifold, deformation equivalent to the 10-dimensional ex- amples constructed by O’Grady. As applications, we show that a birational model of ̃M provides a hyperk ̈ahler compactification of the twisted family of intermediate Jacobians as- sociated to Y . This generalizes the previous result of Voisin [Voi18] in the very general case. We also prove that ̃M is the MRC quotient of the main component of the Hilbert scheme of quintic elliptic curves in Y , confirming a conjecture of Castravet.
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Cubic fourfolds; Stability conditions; Intermediate Jacobian
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/940126`