{"paper":{"title":"Quantization on Curves","license":"","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Christian Fronsdal (UCLA), Maxim Kontsevich (IHES)","submitted_at":"2005-07-07T21:12:28Z","abstract_excerpt":"Deformation quantization on varieties with singularities offers perspectives that are not found on manifolds. Essential deformations are classified by the Harrison component of Hochschild cohomology, that vanishes on smooth manifolds and reflects information about singularities. The Harrison 2-cochains are symmetric and are interpreted in terms of abelian $*$-products. This paper begins a study of abelian quantization on plane curves over $\\Crm$, being algebraic varieties of the form R2/I where I is a polynomial in two variables; that is, abelian deformations of the coordinate algebra C[x,y]/("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0507021","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"}