{"paper":{"title":"Interpolation of Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jorge Ortigas-Galindo, Martin Avendano","submitted_at":"2012-04-13T15:23:12Z","abstract_excerpt":"Let K denote an algebraically closed field. We study the relation between an ideal I in K[x1,...,xn] and its cross sections I_a=I+<x1-a>. In particular, we study under what conditions I can be recovered from the set I_S={(a,I_a):a in S} with S a subset of K. For instance, we show that an ideal I=cap_i Q_i, where Q_i is primary and Q_i cap K[x1]={0}, is uniquely determined by I_S when S is infinite. Moreover, there exists a function B(d,n) such that, if I is generated by polynomials of degree at most d, then I is uniquely determined by I_S when |S|>=B(d,n). If I is also known to be principal, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3027","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"}