On subfiniteness of graded linear series
On subfiniteness of graded linear series
复制标题
关于分级线性级数的亚有限性
DOI：
10.1007/s40879-019-00349-0
复制
发表时间：
2019
影响因子：
0.6
通讯作者：
Ikoma Hideaki
中科院分区：
文献类型：
--
作者：
Chen Huayi;Ikoma Hideaki
希尔伯特第十四问题研究有限型积分代数与该代数的分式域的子域的交的有限生成性质。它有一个否定的答案，由于长田的反例。我们表明，希尔伯特的第十四个问题的一个次有限版本有一个肯定的答案。然后建立了这个结果的一个分次类比，从而证明了分次线性级数的次有限性不依赖于所考虑的函数域，最后，我们将这个结果应用于几何和算术分次线性级数的研究.
Hilbert’s fourteenth problem studies the finite generation property of the intersection of an integral algebra of finite type with a subfield of the fraction field of the algebra. It has a negative answer due to a counterexample of Nagata. We show that a subfinite version of Hilbert’s fourteenth problem has an affirmative answer. We then establish a graded analogue of this result, which permits to show that the subfiniteness of graded linear series does not depend on the function field in which we consider it. Finally, we apply the subfiniteness result to the study of geometric and arithmetic graded linear series.