{"paper":{"title":"The generalized Lelong numbers and intersection theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.DS","math.NT"],"primary_cat":"math.CV","authors_text":"Viet-Anh Nguyen","submitted_at":"2025-01-04T00:46:43Z","abstract_excerpt":"Let $X$ be a complex manifold of dimension $k,$ and $(V,\\omega)$ be a K\\\"ahler submanifold of dimension $l$ in $X,$ and $B\\Subset V$ be a domain with $\\mathcal{C}^2$-smooth boundary. Let $T$ be a positive plurisubharmonic current on $X$ such that $T$ satisfies a reasonable approximation condition on $X$ and near $\\partial B.$ In our previous work we introduce the concept of the generalized Lelong numbers $\\nu_j(T,B)\\in\\mathbb{R}$ of $T$ along $B$ for $0\\leq j\\leq l.$ When $l=0,$ $V=B$ is a single point $x,$ $\\nu_0(T,B)$ is none other than the classical Lelong number of $T$ at $x.$\n  This artic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.02150","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/2501.02150/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"}