{"paper":{"title":"A decomposition formula for J-stability and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Masafumi Hattori","submitted_at":"2021-03-08T08:53:14Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.04603","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.04603/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}