English

A decomposition formula for J-stability and its applications

Algebraic Geometry 2021-03-22 v2 Differential Geometry

Abstract

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

Keywords

Cite

@article{arxiv.2103.04603,
  title  = {A decomposition formula for J-stability and its applications},
  author = {Masafumi Hattori},
  journal= {arXiv preprint arXiv:2103.04603},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-23T23:51:58.587Z