{"paper":{"title":"A sharp lower bound for the log canonical threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Hoang Hiep Pham, Jean-Pierre Demailly (IF)","submitted_at":"2012-01-19T15:38:09Z","abstract_excerpt":"In this note, we prove a sharp lower bound for the log canonical threshold of a plurisubharmonic function $\\varphi$ with an isolated singularity at $0$ in an open subset of ${\\mathbb C}^n$. This threshold is defined as the supremum of constants $c>0$ such that $e^{-2c\\varphi}$ is integrable on a neighborhood of $0$. We relate $c(\\varphi)$ with the intermediate multiplicity numbers $e_j(\\varphi)$, defined as the Lelong numbers of $(dd^c\\varphi)^j$ at $0$ (so that in particular $e_0(\\varphi)=1$). Our main result is that $c(\\varphi)\\ge\\sum e_j(\\varphi)/e_{j+1}(\\varphi)$, $0\\le j\\le n-1$. This ine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4086","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":""},"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"}