论文标题
Jacobian Kummer品种的理性曲线和希尔伯特物业
Rational curves and the Hilbert Property on Jacobian Kummer varieties
论文作者
论文摘要
Corvaja和Zannier的猜想预测，光滑，投影，简单地连接了一个数字字段，其中Zariski密集的合理点具有Hilbert属性。 Demeio证明了与两条椭圆曲线产品相关的Kummer表面。 在本文中，在有限生成的特征零字段中，我们为与jacobian相关的所有Kummer表面建立了Hilbert属性，$ 2 $曲线。总的来说，我们证明所有雅各布kummer品种与奇数$ \ geq 2 $ odg od odg geq 2 $ ods ofd ofd ofd ofd odd off tem off tem the Hilbert属性相关。
A conjecture by Corvaja and Zannier predicts that smooth, projective, simply connected varieties over a number field with Zariski dense set of rational points have the Hilbert Property; this was proved by Demeio for Kummer surfaces which are associated to products of two elliptic curves. In this article, over a finitely generated field of characteristic zero, we establish the Hilbert Property for all Kummer surfaces associated to the Jacobian of a genus $2$ curve. In general we prove that all Jacobian Kummer varieties associated to a hyperelliptic curve of genus $\geq 2$ of odd degree also have the Hilbert Property.
