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- W3108285246 abstract "We prove continuity results for new stability thresholds related to uniform K-stability and deduce that uniform K-stability is an open condition in the Kahler cone of any compact Kahler manifold, thus establishing an algebro-geometric counterpart to a classical result of LeBrun-Simanca for constant scalar curvature (cscK) metrics. This settles a folklore conjecture in the field, and in particular implies openness of uniform K-stability for smooth polarized varieties. Moreover, it strengthens evidence supporting the uniform version of the Yau-Tian-Donaldson conjecture for arbitrary polarizations, including the case of irrational polarizations and non-projective Kahler manifolds. As a key tool we introduce a new norm on test configurations and establish estimates for non-archimedean energy functionals in terms of this norm. This leads to new characterizations of uniform K-stability by restricting to test configurations that satisfy certain uniform bounds. As a byproduct we obtain continuity results for a stability threshold related to non-archimedean entropy and deduce openness of uniform J-stability, as well as openness of J-stability in the projective case." @default.
- W3108285246 created "2020-12-07" @default.
- W3108285246 creator A5078083468 @default.
- W3108285246 date "2020-11-30" @default.
- W3108285246 modified "2023-09-27" @default.
- W3108285246 title "Openness of uniform K-stability in the Kahler cone" @default.
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