论文标题
$χ$ - 体积函数的连续性超过Adelic曲线
The continuity of $χ$-volume functions over adelic curves
论文作者
论文摘要
在Adelic曲线上的Arakelov几何形状的环境中，我们介绍了$χ$ - 体积功能并显示一些一般属性。本文致力于讨论$χ$ - 体积功能的连续性。通过讨论其与音量功能的关系，我们证明了其围绕Adelic $ \ Mathbb {q} $ - afor $ \ mathbb {q} $的连续性 - 卡地亚分数及其连续性及其在微不足道的情况下的连续性。对算术Okounkov身体变化的研究使我们在算术表面上连续扩展。
In the setting of Arakelov geometry over adelic curves, we introduce the $χ$-volume function and show some general properties. This article is dedicated to talk about the continuity of $χ$-volume function. By discussing its relationship with volume function, we prove its continuity around adelic $\mathbb{Q}$-ample $\mathbb{Q}$-Cartier divisors and its continuity in the trivially valued case. The study of the variation of arithmetic Okounkov bodies leads us to its continuous extension on arithmetic surfaces.
