For algebro-geometric study of J-stability, a variant of K-stability, we prove a decomposition formula of non-archimedean J-energy of n-dimensional varieties into n-dimensional intersection numbers rather than $(n+1)$-dimensional ones, and show the equivalence of slope JH-(semi)stability and JH-(semi)stability for surfaces when H is pseudoeffective. Among other applications, we also give a purely algebro-geometric proof of a uniform K-stability of minimal surfaces due to [23], and provides examples which are J-stable (resp., K-stable) but not uniformly J-stable (resp., uniformly K-stable).
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Masafumi Hattori (2025) studied this question.
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