Torsion points of sections of Lagrangian torus fibrations and the Chow ring of hyper-K"ahler fourfolds
Torsion points of sections of Lagrangian torus fibrations and the Chow ring of hyper-K"ahler fourfolds
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拉格朗日环面纤维截面和超K"ahler四重环的Chow环的扭点
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发表时间：
2016
期刊：
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通讯作者：
C. Voisin
中科院分区：
文献类型：
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作者：
C. Voisin
Let $phi：X
ightarrow B$是维度$leq 8 $的投射不可约超K“ahler流形上的拉格朗日纤维化。让$Min {
m Pic}，X$是一个线丛，其对一般纤维$X_B$的限制
$phi$是拓扑平凡的。我们证明了如果纤维化具有最大变差或等平凡，则点集B使得
$M_{mid X_B}$是挠在$B$中稠密的。我们给出了X$的Chow环的一个应用。我们证明了一个类似的结果，椭圆纤维化的玩具模型的参数。
Let $phi:X
ightarrow B$ be a Lagrangian fibration on a projective irreducible hyper-K"ahler manifold of dimension $leq8$. Let $Min {
m Pic},X$ be a line bundle whose restriction to the general fiber $X_b$ of
$phi$ is topologically trivial. We prove that if the fibration has maximal variation or is isotrivial, the set of points $b$ such that the restriction
$M_{mid X_b}$ is torsion is dense in $B$. We give an application to the Chow ring of $X$. We prove a similar result for elliptic fibrations which gives a toy model for the argument.