We show that a general ordinary Gushel–Mukai (GM) threefold can be reconstructed from its Kuznetsov component together with an extra piece of data coming from tautological subbundle of the Grassmannian . We also prove that determines the birational isomorphism class of , while determines the isomorphism class of a special GM threefold if it is general. As an application, we prove a conjecture of Kuznetsov–Perry in dimension 3 under a mild assumption. Finally, we use to restate a conjecture of Debarre–Iliev–Manivel regarding fibers of the period map for ordinary GM threefolds.

中文翻译：

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Gushel-Mukai 三重的分类 Torelli 定理

我们证明了一般普通 Gushel-Mukai (GM) 的三倍可以从其库兹涅佐夫组件重建以及来自格拉斯曼函数的同义反复子丛的额外数据。我们还证明决定了双有理同构类， 尽管确定特殊 GM 的三重同构类如果是一般的话。作为一个应用，我们在温和的假设下证明了 3 维库兹涅佐夫-佩里猜想。最后，我们使用重申 Debarre-Iliev-Manivel 关于普通 GM 三重周期图纤维的猜想。