For a general cubic fourfold, it was observed by Donagi and Markman that the relative intermediate Jacobian fibration associated to the family of its hyperplane sections carries a natural holomorphic symplectic form making the fibration Lagrangian. In this paper, we obtain a smooth projective compactification of the intermediate Jacobian fibration giving a ten-dimensional compact hyper-K\"ahler manifold, which we then show to be deformation equivalent to the exceptional example of O'Grady. This proves a conjecture by Markushevich.

中文翻译：

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与立方 4 倍相关的中间雅可比纤维化的超 Kähler 压缩

对于一般的四倍体，Donagi 和 Markman 观察到与其超平面截面族相关的相对中间雅可比纤维化具有自然的全纯辛形式，从而形成纤维化拉格朗日。在本文中，我们获得了中间雅可比颤动的平滑投影紧致，给出了一个十维紧致的超 K\"ahler 流形，然后我们证明它是变形等效于 O'Grady 的特殊例子。这证明了一个猜想马库舍维奇。