{"paper":{"title":"The Initial Degree of Symbolic Powers of Ideals of Fermat Configuration of Points","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Thai Thanh Nguyen","submitted_at":"2021-01-28T22:38:00Z","abstract_excerpt":"Let $n \\ge 2$ be an integer and consider the defining ideal of the Fermat configuration of points in $\\mathbb{P}^2$: $I_n=(x(y^n-z^n),y(z^n-x^n),z(x^n-y^n)) \\subset R=\\mathbb{C}[x,y,z]$. In this paper, we compute explicitly the least degree of generators of its symbolic powers in all unknown cases. As direct applications, we easily verify Chudnovsky's Conjecture, Demailly's Conjecture and Harbourne-Huneke Containment problem as well as calculating explicitly the Waldschmidt constant and (asymptotic) resurgence number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.12308","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.12308/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}