Maximal divisorial sets in arc spaces

A Hilbert-Mumford criterion for SL_2-actions

Let the special linear group $G := SL_{2}$ act regularly on a $Q$-factorial variety $X$. Consider a maximal torus $T \subset G$ and its normalizer $N \subset G$. We prove: If $U \subset X$ is a maximal open $N$-invariant subset admitting a good quotient $U \to U // N$ with a divisorial quotient space, then the intersection $W(U)$ of all translates $g \dot U$ is open in $X$ and admits a good quotient $W(U) \to W(U) // G$ with a divisorial quotient space. Conversely, we obtain that every maximal open $G$-invariant subset $W \subset X$ admitting a good quotient $W \to W // G$ with a divisorial qu…

关于子水平集体积渐近性的除子几何

On the Divisorial Geometry of Volume Asymptotics of Sublevel Sets

本文通过子水平集的体积渐近行为，揭示了实对数规范阈值的除子谱，并给出了弧空间上的内在解释，表明除子不变量具有度量实现。

抽象除数空间与算术交数

Abstract divisorial spaces and arithmetic intersection numbers

本文引入抽象除数空间，用于推广算术交数至Chen和Moriwaki意义下的proper adelic基曲线，同时允许非阿基米德地方使用相对混合能量的更奇异度量。

K-稳定性的非阿基米德方法，I：测试构型与赋值的度量几何

A non-Archimedean approach to K-stability, I: Metric geometry of spaces of test configurations and valuations

本文用非阿基米德方法研究K-稳定性，通过Berkovich解析化上的Fubini-Study函数刻画测试构型空间，并建立除子范数与除子测度的一一对应。

Arcs, valuations and the Nash map

This paper gives a map from the set of families of arcs on a variety to the set of valuations on the rational function field of the variety We characterize a family of arcs which corresponds to a divisorial valuation by this map. We can see that both the Nash map and a certain McKay correspondence are the restrictions of this map. This paper also gives the affirmative answer to the Nash problem for a non-normal variety in a certain category. As a corollary, we get the affirmative answer for a non-normal toric variety.

Drinfeld-Grinberg-Kazhdan定理与弧空间的嵌入余维数

The Drinfeld-Grinberg-Kazhdan theorem and embedding codimension of the arc space

论文扩展了Drinfeld, Grinberg和Kazhdan定理至任意余代数的弧，并证明了非奇异位势的不可约子集的嵌入余维数在通用情况下恒定。同时将最大除数集的有限形式模型与底层变种的奇点不变量联系起来。