论文标题
立方四倍的中间雅各布振动的耶和华几何形状
Birational geometry of the intermediate Jacobian fibration of a cubic fourfold
论文作者
论文摘要
我们表明，与任何平滑立方四倍$ x $相关的中间雅各布纤维纤维均与常规的lagrangian纤维化$ j \ to \ mathbb p^5 $相关。这建立在Arxiv：1602.05534的基础上，其中证明了一般$ x $的结果，以及ARXIV上的退化技术：1704.02731及其最小模型计划中的技术。 We then study some aspects of the birational geometry of $J(X)$: for very general $X$ we compute the movable and nef cones of $J(X)$, showing that $J(X)$ is not birational to the twisted version of the intermediate Jacobian fibration arXiv:1611.06679, nor to an OG$10$-type moduli space of objects in the Kuznetsov component of $ x $;对于任何平稳的$ x $，我们使用普通功能显示，Abelian纤维的Mordell-Weil group $ mw（π）$ $π： z）_0 $。
We show that the intermediate Jacobian fibration associated to any smooth cubic fourfold $X$ admits a hyper-Kähler compactification $J(X)$ with a regular Lagrangian fibration $J \to \mathbb P^5$. This builds upon arXiv:1602.05534, where the result is proved for general $X$, as well as on the degeneration techniques on arXiv:1704.02731 and techniques from the minimal model program. We then study some aspects of the birational geometry of $J(X)$: for very general $X$ we compute the movable and nef cones of $J(X)$, showing that $J(X)$ is not birational to the twisted version of the intermediate Jacobian fibration arXiv:1611.06679, nor to an OG$10$-type moduli space of objects in the Kuznetsov component of $X$; for any smooth $X$ we show, using normal functions, that the Mordell-Weil group $MW(π)$ of the abelian fibration $π: J \to \mathbb P^5$ is isomorphic to the integral degree $4$ primitive algebraic cohomology of $X$, i.e., $MW(π) = H^{2,2}(X, \mathbb Z)_0$.
