标题： 关于分级线性序列的耦合稳定性阈值 显示英文标题

标题： On the coupled stability thresholds of graded linear series

摘要： 本文中，我们研究了分级线性系的一些基本性质。 首先我们看到，如果一个分级线性系包含一个丰沛系，则在双有理态射下的系统拉回也是丰沛的。 利用这一命题，我们定义了关于原始旗的分级线性系的细化，并给出了计算这些细化的$S$- 不变量的一些公式。 其次，我们引入了分级线性系的耦合稳定性阈值的概念，这是由 Rubinstein--Tian--Zhang 提出的概念的推广。 我们看到，在有限数量的包含丰沛系的分级线性系的支持集内部，耦合稳定性阈值函数可以唯一地连续延拓，这推广了张克威的工作。 第三，我们得到了耦合稳定性阈值的乘积型公式，这是 Zhuang 工作的推广。 第四，我们看到了类似于 Abban--Zhuang 的用于估计局部耦合稳定性阈值的公式。 显示英文摘要

摘要： In this paper, we see several basic properties of graded linear series. We firstly see that, if a graded linear series contains an ample series, then so are the pullbacks of the system under birational morphisms. Using this proposition, we define the refinements of graded linear series with respects to primitive flags. Moreover, we give several formulas to compute the $S$-invariant of those refinements. Secondly, we introduce the notion of coupled stability thresholds for graded linear series, which is a generalization of the notion introduced by Rubinstein--Tian--Zhang. We see that, over the interior of the support for finite numbers of graded linear series containing an ample series, the coupled stability threshold function can be uniquely extended continuously, which generalizes the work by Kewei Zhang. Thirdly, we get a product-type formula for coupled stability thresholds, which generalizes the work of Zhuang. Fourthly, we see Abban--Zhuang's type formulas for estimating local coupled stability thresholds.