{"paper":{"title":"Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part I","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"F. Reese Harvey, H. Blaine Lawson Jr","submitted_at":"2005-12-15T21:25:59Z","abstract_excerpt":"We introduce the notion of the projective linking number Link(M,Z) of a compact oriented real submanifold M of dimension 2p-1 in complex projective n-space P^n with an algebraic subvariety Z in P^n - M of codimension p. This notion is related to projective winding numbers and quasi-plurisubharmonic functions, and it generalizes directly from P^n to any projective manifold. Part 1 of this paper establishes the following result for the case p=1. Let M be an oriented, stable, real analytic curve in P^n. Then M is the boundary of a positive holomorphic 1-chain T with Mass(T) < K in P^n if and only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512379","kind":"arxiv","version":4},"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"}