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A transcendental approach to non-Archimedean metrics of pseudoeffective classes
- Publication Year :
- 2023
-
Abstract
- We introduce the concept of non-Archimedean metrics attached to a transcendental pseudoeffective cohomology class on a compact K\"ahler manifold. This is obtained via extending the Ross-Witt Nystr\"om 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.<br />Comment: v.2 references updated. Presentation improved v.3 accepted version
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2302.02541
- Document Type :
- Working Paper