超越方法用于伪有效类的非阿基米德度量
A transcendental approach to non-Archimedean metrics of pseudoeffective classes
AI总结：
本文提出了一种超越方法，用于研究伪有效类的非阿基米德度量，并通过旗帜配置和滤子刻画了delta不变量，证明了YTD类型的存在定理。
摘要：
我们引入了一个与紧凯勒流形上的超越伪有效上同调类相关的非阿基米德度量的概念。这是通过将Ross-Witt Nyström对应关系扩展到相对情况而获得的，我们指出我们的构造在类由伪有效有理线丛诱导时与Boucksom-Jonsson的构造一致。我们引入了与超越大类相关的旗帜配置的概念，恢复了在大情况下测试配置的概念。我们证明非阿基米德有限能量度量可以由旗帜配置近似，并且非常一般的径向Ding能量是连续的，即使在大情况下这也是一个新的结果。作为应用，我们刻画了delta不变量作为旗帜配置和滤子的Ding半稳定性阈值，并证明了以旗帜配置为术语的YTD类型存在定理。
英文摘要：
We introduce the concept of non-Archimedean metrics attached to a transcendental pseudoeffective cohomology class on a compact Kähler manifold. This is obtained via extending the Ross-Witt Nyström correspondence to the relative case, and we point out that our construction agrees with that of Boucksom-Jonsson when the class is induced by a pseudoeffective $\mathbb Q$-line bundle. We introduce the notion of a flag configuration attached to a transcendental big class, recovering the notion of a test configuration in the ample case. We show that non-Archimedean finite energy metrics are approximable by flag configurations, and very general versions of the radial Ding energy are continuous, a novel result even in the ample case. As applications, we characterize the delta invariant as the Ding semistability threshold of flag configurations and filtrations and prove a YTD type existence theorem in terms of flag configurations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
