论文标题
立方四倍，奥格雷迪10和拉格朗日纤维上的椭圆五重奏
Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations
论文作者
论文摘要
对于平滑的立方四倍y，我们研究了y mukai矢量$2λ_1+2λ_2$在Y的Kuznetsov组件中的模量空间M。我们表明，在稳定条件的某个选择下，M承认，符号分辨率$ \\ tilde M $是一种平稳的预期，这是一个平稳的预期，这是一个平稳的构建效果。奥格雷迪。作为应用程序，我们表明，$ \ tilde m $的异性模型提供了与Y相关的中间雅各布人的扭曲家族的HyperKähler压缩。这在非常笼统的情况下概括了Voisin arxiv：1611.06679的先前结果。我们还证明，$ \ tilde m $是y椭圆形曲线希尔伯特计划的主要组成部分的MRC商，证实了Castravet的猜想。
For a smooth cubic fourfold Y, we study the moduli space M of semistable objects of Mukai vector $2λ_1+2λ_2$ 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 hyperkähler 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 hyperkähler 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.
