A decomposition formula for J-stability and its applications

Abstract

For algebro-geometric study of J-stability, a variant of K-stability, we prove a decomposition formula of non-archimedean $\mathcal{J}$-energy of $n$-dimensional varieties into $n$-dimensional intersection numbers rather than $(n+1)$-dimensional ones, and show the equivalence of slope ${\mathrm{J}}^H$-(semi)stability and ${\mathrm{J}}^H$-(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).

v2:added some citations, emphasized the difference between J-positivity and J-stability

References in corpus (3)

• K-stability and Kähler-Einstein metrics
• Extremal metrics and K-stability (PhD thesis)
• Nakai-Moishezon criterions for complex Hessian equations