{"paper":{"title":"Stability of test ideals of divisors with small multiplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kenta Sato","submitted_at":"2016-02-09T14:28:47Z","abstract_excerpt":"Let $(X, \\Delta)$ be a log pair in characteristic $p>0$ and $P$ be a (not necessarily closed) point of $X$. We show that there exists a constant $\\delta>0$ such that $\\tau(X, \\Delta)_P= \\tau(X, \\Delta + D)_P$ for each effective $\\mathbb{Q}$-Cartier divisor $D$ with $\\mathrm{mult}_P(D) <\\delta$. As its application, we show that if $D$ is an $\\mathbb{R}$-Cartier divisor on a strongly $F$-regular projective variety, then the non-nef locus of $D$ coincides with the restricted base locus of $D$. This is a generalization of a result of Musta\\c{t}\\v{a} to the singular case and can be viewed as a char"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02996","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"}