{"paper":{"title":"Siu's analyticity theorem for positive pluriharmonic currents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Tien-Cuong Dinh, Viet-Anh Nguyen","submitted_at":"2026-06-29T01:05:21Z","abstract_excerpt":"Let $T$ be a positive $\\ddc$-closed current of bidimension $(1,1)$ on a projective manifold $X$ of dimension $n.$ We show that for every $c > 0$ the set of points of $X$ where the Lelong number of $T$ is larger or equal to $c$ is an analytic subset of dimension at most $1$ of $X.$ Moreover, the following Siu decomposition holds $$T=\\sum_{i\\in I} \\lambda_i[V_i] +T_0,$$ where $\\{V_i\\}_{i\\in I}$ is a (possibly empty) finite or countable family of compact analytic curves in $X,$ $\\lambda_i\\in\\mathbb{R}^+,$ and $T_0$ is a positive $\\ddc$-closed current of bidimension $(1,1)$ on $X$ whose Lelong num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29680","kind":"arxiv","version":1},"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/2606.29680/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"}