{"paper":{"title":"Green functions with singularities along complex spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A. Rashkovskii, R. Sigurdsson","submitted_at":"2004-08-30T13:09:01Z","abstract_excerpt":"We study properties of a Green function G_A with singularities along a complex subspace A of a complex manifold X. It is defined as the largest negative plurisubharmonic function u satisfying locally u\\leq \\log|\\psi|+C, where \\psi=(\\psi_1, ...,\\psi_m), \\psi_1, ...,\\psi_m are local generators for the ideal sheaf I_A of A, and C is a constant depending on the function u and the generators. A motivation for this study is to estimate global bounded functions from the sheaf I_A and thus proving a ``Schwarz Lemma'' for I_A."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408407","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":""},"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"}