{"paper":{"title":"Freeness of Conic-Line Arrangements in $\\mathbb P^2$","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Hal Schenck, Stefan O. Tohaneanu","submitted_at":"2007-09-12T14:40:58Z","abstract_excerpt":"Let ${\\mathcal C}= \\bigcup_{i=1}^n C_i \\subseteq \\mathbb{P}^2$ be a collection of smooth rational plane curves. We prove that the addition-deletion operation used in the study of hyperplane arrangements has an extension which works for a large class of arrangements of smooth rational curves, giving an inductive tool for understanding the freeness of the module $\\Omega^1({\\mathcal C})$ of logarithmic differential forms with pole along ${\\mathcal C}$. We also show that the analog of Terao's conjecture (freeness of $\\Omega^1({\\mathcal C})$ is combinatorially determined if ${\\mathcal C}$ is a unio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1890","kind":"arxiv","version":1},"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"}