A decomposition formula for Jstability and its applications
Abstract
For algebrogeometric study of Jstability, a variant of Kstability, we prove a decomposition formula of nonarchimedean $\mathcal{J}$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 algebrogeometric proof of a uniform Kstability of minimal surfaces due to [23], and provides examples which are Jstable (resp., Kstable) but not uniformly Jstable (resp., uniformly Kstable).
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 DOI:
 10.48550/arXiv.2103.04603
 arXiv:
 arXiv:2103.04603
 Bibcode:
 2021arXiv210304603H
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Differential Geometry
 EPrint:
 v2:added some citations, emphasized the difference between Jpositivity and Jstability