{"paper":{"title":"Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.AG","authors_text":"Alex Chirvasitu, Ryo Kanda, S. Paul Smith","submitted_at":"2019-08-18T22:32:02Z","abstract_excerpt":"The elliptic algebras in the title are connected graded $\\mathbb{C}$-algebras, denoted $Q_{n,k}(E,\\tau)$, depending on a pair of relatively prime integers $n>k\\ge 1$, an elliptic curve $E$, and a point $\\tau\\in E$. This paper examines a canonical homomorphism from $Q_{n,k}(E,\\tau)$ to the twisted homogeneous coordinate ring $B(X_{n/k},\\sigma',\\mathcal{L}'_{n/k})$ on the characteristic variety $X_{n/k}$ for $Q_{n,k}(E,\\tau)$. When $X_{n/k}$ is isomorphic to $E^g$ or the symmetric power $S^gE$ we show the homomorphism $Q_{n,k}(E,\\tau) \\to B(X_{n/k},\\sigma',\\mathcal{L}'_{n/k})$ is surjective, tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06525","kind":"arxiv","version":3},"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/1908.06525/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"}