Hilbert's 14th problem over finite fields and a conjecture on the cone of curves
Hilbert's 14th problem over finite fields and a conjecture on the cone of curves
复制标题
希尔伯特有限域第十四个问题和曲线锥猜想
DOI：
10.1112/s0010437x08003667
复制
发表时间：
2008
影响因子：
1.8
通讯作者：
Totaro B
中科院分区：
文献类型：
--
作者：
Totaro B
我们给出了非有限生成的不变量环的有限域上的第一个例子。(这些示例适用于任意字段，例如有理数。)所涉及的基团可以小到添加剂基团的三个拷贝。有限生成的失败来自于某些具有正Mordell-Weil秩的椭圆原纤维或阿贝尔表面原原纤维。我们的工作是把Calabi-Yau纤维空间上的Morison-Kawamata锥猜想推广到Kt Calabi-Yau对上。在反正则丛是半充分的假设下，我们证明了二维猜想。
We give the first examples over finite fields of rings of invariants that are not finitely generated. (The examples work over arbitrary fields, for example the rational numbers.) The group involved can be as small as three copies of the additive group. The failure of finite generation comes from certain elliptic fibrations or abelian surface fibrations having positive Mordell–Weil rank. Our work suggests a generalization of the Morrison–Kawamata cone conjecture on Calabi–Yau fiber spaces to klt Calabi–Yau pairs. We prove the conjecture in dimension two under the assumption that the anticanonical bundle is semi-ample.