{"paper":{"title":"Chudnovsky's Conjecture and the stable Harbourne-Huneke containment for general points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Sankhaneel Bisui, Th\\'ai Th\\`anh Nguy\\^en","submitted_at":"2021-12-31T01:21:18Z","abstract_excerpt":"In our previous work with Grifo and H\\`a, we showed the stable Harbourne-Huneke containment and Chudnovsky's conjecture for the defining ideal of sufficiently many general points in $\\mathbb{P}^N$. In this paper, we establish the conjectures for all remaining cases, and hence, give the affirmative answer to Harbourne-Huneke containment and Chudnovsky's conjecture for any number of general points in $\\mathbb{P}^N$ for all $N$. Our new technique is to develop the Cremona reduction process that provides effective lower bounds for the Waldschmidt constant of the defining ideals of generic points i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.15260","kind":"arxiv","version":3},"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/2112.15260/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"}