Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations
Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations
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DOI：
10.1016/j.aim.2022.108584
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发表时间：
2020-07
影响因子：
1.7
通讯作者：
Chunyi Li;L. Pertusi;Xiaolei Zhao
中科院分区：
文献类型：
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作者：
Chunyi Li;L. Pertusi;Xiaolei Zhao
对于光滑三次四重Y，研究了Y的Kuznetsov分量中Mukai向量2 λ 1 + 2 λ 2的半稳定对象的模空间M.我们表明，与一定的选择的稳定性条件，M承认一个辛决议M，这是一个光滑的射影hyperkähler流形，变形相当于10维的例子构造的奥格雷迪。作为应用，我们证明了M的双有理模型提供了与Y相关联的扭曲的中间Jacobian族的超kähler紧化。这在非常一般的情况下推广了Voisin [58]以前的结果。我们还证明了M是Y中五次椭圆曲线的Hilbert格式的主分支的MRC商，证实了Castravet的一个猜想。
For a smooth cubic fourfold Y, we study the moduli space M of semistable objects of Mukai vector 2 λ 1+ 2 λ 2 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 hyperkähler manifold, deformation equivalent to the 10-dimensional examples constructed by O'Grady. As applications, we show that a birational model of M˜ provides a hyperkähler compactification of the twisted family of intermediate Jacobians associated to Y. This generalizes the previous result of Voisin [58] 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.