{"paper":{"title":"Obstructions to Deformation Quantization of Bundles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP","quant-ph"],"primary_cat":"math.AG","authors_text":"Greg Huey, Vladimir Baranovsky","submitted_at":"2026-07-14T15:43:48Z","abstract_excerpt":"Let $\\left(M, \\mathcal{O}_M \\right)$ be a smooth algebraic variety over field $\\kappa$ of characteristic $0$ with an algebraic symplectic form $\\omega$, or a complex manifold with a holomorphic form $\\omega$. Furthermore, let $E$ be a vector bundle over $\\left(M, \\mathcal{O}_M \\right)$ and $\\mathcal{O}_{\\hbar}$ a deformation quantization of $\\mathcal{O}_M$ compatible with $\\omega$.\n  Assuming that $E$ possesses a deformation quantization to order $\\hbar^k$ we consider the problem of extending it to order $\\hbar^\\ell$ for $\\ell > k$, and establish triviality of an obstruction class as a necessa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12910","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.12910/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"}