A transcendental approach to non-Archimedean metrics of pseudoeffective classes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911351039852544 |
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| author | Darvas, Tamás Xia, Mingchen Zhang, Kewei |
| author_facet | Darvas, Tamás Xia, Mingchen Zhang, Kewei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02541 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A transcendental approach to non-Archimedean metrics of pseudoeffective classes Darvas, Tamás Xia, Mingchen Zhang, Kewei Algebraic Geometry Complex Variables Differential Geometry 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. |
| title | A transcendental approach to non-Archimedean metrics of pseudoeffective classes |
| topic | Algebraic Geometry Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2302.02541 |