{"paper":{"title":"Hochschild cohomology of algebras of differential operators tangent to a central arrangement of lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Francisco Kordon, Mariano Su\\'arez-\\'Alvarez","submitted_at":"2018-07-26T21:30:19Z","abstract_excerpt":"Given a central arrangement of lines $\\mathcal{A}$ in a $2$-dimensional vector space $V$ over a field of characteristic zero, we study the algebra $\\mathcal D(\\mathcal A)$ of differential operators on $V$ which are logarithmic along $\\mathcal A$. Among other things we determine the Hochschild cohomology of $\\mathcal D(\\mathcal A)$ as a Gerstenhaber algebra, establish a connection between that cohomology and the de Rham cohomology of the complement $M(\\mathcal A)$ of the arrangement, determine the isomorphism group of $\\mathcal D(\\mathcal A)$ and classify the algebras of that form up to isomorp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10372","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"}