{"paper":{"title":"On Segre's bound for fat points in $\\mathbb{P}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Edoardo Ballico, Elisa Postinghel, Olivia Dumitrescu","submitted_at":"2015-04-20T18:41:01Z","abstract_excerpt":"For a scheme of fat points $Z$ defined by the saturated ideal $\\mathcal{I}_Z$, the regularity index computes the Castelnuovo-Mumford regularity of the Cohen-Macaulay ring $R/\\mathcal{I}_Z.$ For points in \" general position\" we improve the bound for the regularity index computed by Segre for $\\mathbb {P}^2$ and generalised by Catalisano, Trung and Valla for $\\mathbb {P}^n$. Moreover, we prove that the generalised Segre's bound conjectured by Fatabbi and Lorenzini holds for $n+3$ arbitrary points in $\\mathbb {P}^n$. We propose a modification of Segre's conjecture for arbitrary points and we disc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05151","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"}