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arXiv · 2007.14108

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

Chunyi Li·Laura Pertusi·Xiaolei Zhao
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Abstract

For a smooth cubic fourfold Y, we study the moduli space M of semistable objects of Mukai vector $2\lambda_1+2\lambda_2$ in the Kuznetsov component of Y. We show that with a certain choice of stability conditions, M admits a symplectic resolution $\tilde M$, which is a smooth projective hyperk\"ahler manifold, deformation equivalent to the 10-dimensional examples constructed by O'Grady. As applications, we show that a birational model of $\tilde M$ provides a hyperk\"ahler compactification of the twisted family of intermediate Jacobians associated to Y. This generalizes the previous result of Voisin arXiv:1611.06679 in the very general case. We also prove that $\tilde M$ is the MRC quotient of the main component of the Hilbert scheme of elliptic quintic curves in Y, confirming a conjecture of Castravet.

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Chunyi Li, Laura Pertusi, Xiaolei Zhao. 2020-07-28. Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations. https://arxiv.org/abs/2007.14108

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