K-stability and Fujita approximation.(English)Zbl 1540.32010
Cheltsov, Ivan (ed.) et al., Birational geometry, Kähler-Einstein metrics and degenerations. Proceedings of the conferences, Moscow, Russia, April 8–13, 2019, Shanghai, China, June 10–14, 2019, Pohang, South Korea, November 18–22, 2019. Cham: Springer. Springer Proc. Math. Stat. 409, 545-566 (2023).
Summary: This note is a continuation to the paper [C. Li, “Geodesic rays and stability in the cscK problem”, Ann. Sci. Éc. Norm. Supér. (4) (accepted),arXiv:2001.01366]. We derive a formula for non-Archimedean Monge-Ampère measures of big models. As applications, we derive a positive intersection formula for non-Archimedean Mabuchi functional, and further reduces the \((\operatorname{Aut}(X, L)_0)\)-uniform Yau-Tian-Donaldson conjecture for polarized manifolds to a conjecture on the existence of approximate Zariski decompositions that satisfy some asymptotic vanishing condition. In an appendix, we also verify this conjecture for some of Nakayama’s examples that do not admit birational Zariski decompositions.
For the entire collection see [Zbl 1515.14010].
For the entire collection see [Zbl 1515.14010].
MSC:
| 32Q15 | Kähler manifolds |
| 14E30 | Minimal model program (Mori theory, extremal rays) |
| 32P05 | Non-Archimedean analysis |
| 32Q26 | Notions of stability for complex manifolds |
Cite
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