{"paper":{"title":"Fermat-type configurations of lines in $\\mathbb P^3$ and the containment problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.AG","authors_text":"Grzegorz Malara, Justyna Szpond","submitted_at":"2017-02-07T19:01:18Z","abstract_excerpt":"The purpose of this note is to show a new series of examples of homogeneous ideals $I$ in ${\\mathbb K}[x,y,z,w]$ for which the containment $I^{(3)}\\subset I^2$ fails. These ideals are supported on certain arrangements of lines in ${\\mathbb P}^3$, which resemble Fermat configurations of points in ${\\mathbb P}^2$, see \\cite{NagSec16}. All examples exhibiting the failure of the containment $I^{(3)}\\subseteq I^2$ constructed so far have been supported on points or cones over configurations of points. Apart of providing new counterexamples, these ideals seem quite interesting on their own."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02160","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"}