发表机构
The Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了双有理最小斜率下J-方程解的存在性、唯一性与局部正则性，引入解析阈值并利用Bergman核逼近给出J-零轨迹的解析刻画，证实了Datar--Mete--Song猜想。
AI 中文摘要
我们证明了在双有理最小斜率下，求解J-方程的Kähler current的存在性、唯一性以及在适当解析子集之外的局部正则性。这证实了Datar--Mete--Song在\\(\cite{DMS26}\\)中的猜想1.5。我们引入了一个解析阈值，并证明了它与Datar--Mete--Song引入的双有理阈值等价。关键工具之一是利用Bergman核来逼近子解，这一方法受Demailly关于具有解析奇点的多次调和函数逼近工作的启发。作为Bergman核逼近的一个应用，我们结合Fang--Ma \\(\cite{FM26}\\)的结果，给出了半稳定对\\((\alpha,\beta)\\)的\\(J\\)-零轨迹的解析刻画。这消除了\\(\cite{L26b}\\)中的技术假设。
英文摘要
We prove the existence, uniqueness, and partial regularity outside a proper analytic subset for the Kähler current solving the $J$-equation at the birational minimal slope. This confirms Datar--Mete--Song's conjecture 1.5 in \cite{DMS26}. We introduce an analytic threshold, and prove its equivalence to the birational threshold introduced by Datar--Mete--Song. One of the key tools is the approximation of subsolution by Bergman's kernels, which is motivated by the work of Demailly on the approximation of plurisubharmonic functions with analytic singularities. As an application of the Bergman kernel approximation, we combine the results of Fang--Ma \cite{FM26} to give an analytic characterization of the $J$-null locus of a semistable pair $(α,β)$. This removes the technical assumptions in \cite{L26b}.
