{"paper":{"title":"Green functions, Segre numbers, and King's formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Elizabeth Wulcan, Mats Andersson","submitted_at":"2013-04-29T14:41:35Z","abstract_excerpt":"Let $\\mathcal J$ be a coherent ideal sheaf on a complex manifold $X$ with zero set $Z$, and let $G$ be a plurisubharmonic function such that $G=\\log|f|+\\mathcal O(1)$ locally at $Z$, where $f$ is a tuple of holomorphic functions that defines $\\mathcal J$. We give a meaning to the Monge-Amp\\`{e}re products $(dd^c G)^k$ for $k=0,1,2,...$, and prove that the Lelong numbers of the currents $M_k^{\\mathcal J}:=\\mathbf 1_Z(dd^c G)^k$ at $x$ coincide with the so-called Segre numbers of $\\mathcal J$ at $x$, introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7675","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}