{"paper":{"title":"Rational Singularities and Uniform Symbolic Topologies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Robert M. Walker","submitted_at":"2015-10-10T23:58:35Z","abstract_excerpt":"Take $(R, \\mathfrak{m})$ any normal Noetherian domain, either local or $\\mathbb{N}$-graded over a field. We study the question of when $R$ satisfies the uniform symbolic topology property (USTP) of Huneke, Katz, and Validashti: namely, that there exists an integer $D>0$ such that for all prime ideals $P \\subseteq R$, the symbolic power $P^{(Da)} \\subseteq P^a$ for all $a >0$. Reinterpreting results of Lipman, we deduce that when $R$ is a two-dimensional rational singularity, then it satisfies the USTP. Emphasizing the non-regular setting, we produce explicit, effective multipliers $D$, working"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02993","kind":"arxiv","version":2},"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"}