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).
- Publication:
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arXiv e-prints
- Pub Date:
- March 2021
- DOI:
- 10.48550/arXiv.2103.04603
- arXiv:
- arXiv:2103.04603
- Bibcode:
- 2021arXiv210304603H
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Differential Geometry
- E-Print:
- v2:added some citations, emphasized the difference between J-positivity and J-stability