{"paper":{"title":"Directed unions of local quadratic transforms of regular local rings and pullbacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bruce Olberding, Lorenzo Guerrieri, Matt Toeniskoetter, William Heinzer","submitted_at":"2017-02-10T03:36:39Z","abstract_excerpt":"Let $\\{ R_n, {\\mathfrak m}_n \\}_{n \\ge 0}$ be an infinite sequence of regular local rings with $R_{n+1}$ birationally dominating $R_n$ and ${\\mathfrak m}_nR_{n+1}$ a principal ideal of $R_{n+1}$ for each $n$. We examine properties of the integrally closed local domain $S = \\bigcup_{n \\ge 0}R_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03058","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"}