{"paper":{"title":"Picard Groups of Normal Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"John Brevik, Scott Nollet","submitted_at":"2012-08-01T16:47:22Z","abstract_excerpt":"We study the fixed singularities imposed on members of a linear system of surfaces in P^3_C by its base locus Z. For a 1-dimensional subscheme Z \\subset P^3 with finitely many points p_i of embedding dimension three and d >> 0, we determine the nature of the singularities p_i \\in S for general S in |H^0 (P^3, I_Z (d))| and give a method to compute the kernel of the restriction map Cl S \\to Cl O_{S,p_i}. One tool developed is an algorithm to identify the type of an A_n singularity via its local equation. We illustrate the method for representative Z and use Noether-Lefschetz theory to compute P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0269","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"}