论文标题
k稳定性的一种非一切集的方法，ii：分区稳定性和开放性
A non-Archimedean approach to K-stability, II: divisorial stability and openness
论文作者
论文摘要
对于任何投影对$（x，b）$，配备了足够的$ \ m athbb {q} $ - 线束$ l $（甚至任何足够的数值类），我们附上一个新的不变$β（μ）\ in \ mathbb {r} $，在convex Compination $ $ x上定义了$ x $ x $ x $ x $ x $ x $ x $ x $ x的$β（μ）\ $ x $。该构建基于非Archimedean Pluripential理论，并扩展了Dervan-Legendre不变性以进行单个估值 - 本身专门针对Li和Fujita在FANO案例中的评估不变性，该案例检测到K稳定性。使用我们的$β$ invariant，我们定义了分区（半）稳定性，并表明分数的可准性性意味着$（x，b）$是sublc（即其日志差异函数是非负函数），而分数稳定性是与极化$ l $ l $ l $相对于偏离的开放条件。我们还表明，除了（充足）测试配置的通常意义上，分区稳定性意味着统一的k稳定性，并且相当于$（x，l）$的所有规范/过滤的统一K稳定性，如Chi Li所考虑的。
To any projective pair $(X,B)$ equipped with an ample $\mathbb{Q}$-line bundle $L$ (or even any ample numerical class), we attach a new invariant $β(μ)\in\mathbb{R}$, defined on convex combinations $μ$ of divisorial valuations on $X$, viewed as point masses on the Berkovich analytification of $X$. The construction is based on non-Archimedean pluripotential theory, and extends the Dervan-Legendre invariant for a single valuation--itself specializing to Li and Fujita's valuative invariant in the Fano case, which detects K-stability. Using our $β$-invariant, we define divisorial (semi)stability, and show that divisorial semistability implies $(X,B)$ is sublc (i.e. its log discrepancy function is non-negative), and that divisorial stability is an open condition with respect to the polarization $L$. We also show that divisorial stability implies uniform K-stability in the usual sense of (ample) test configurations, and that it is equivalent to uniform K-stability with respect to all norms/filtrations on the section ring of $(X,L)$, as considered by Chi Li.
