{"paper":{"title":"Uniform Harbourne-Huneke Bounds via Flat Extensions","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":"2016-08-08T05:18:25Z","abstract_excerpt":"Over an arbitrary field $\\mathbb{F}$, Harbourne conjectured that $$I^{(N (r-1)+1)} \\subseteq I^r$$ for all $r>0$ and all homogeneous ideals $I$ in $S = \\mathbb{F} [\\mathbb{P}^N] = \\mathbb{F} [x_0, \\ldots, x_N]$. The conjecture has been disproven for select values of $N \\ge 2$: first by Dumnicki, Szemberg, and Tutaj-Gasi\\'{n}ska in characteristic zero, and then by Harbourne and Seceleanu in odd positive characteristic. However, the ideal containments above do hold when, for instance, $I$ is a monomial ideal in $S$.\n  As a sequel to (arXiv:1510.02993), we present criteria for containments of typ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02320","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"}