{"paper":{"title":"The Ext algebra of a quantized cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Damien Calaque, Julien Grivaux","submitted_at":"2017-11-26T15:17:27Z","abstract_excerpt":"Given a quantized analytic cycle $(X, \\sigma)$ in $Y$, we give a categorical Lie-theoretic interpretation of a geometric condition, discovered by Shilin Yu, that involves the second formal neighbourhood of $X$ in $Y$. If this condition (that we call tameness) is satisfied, we prove that the derived Ext algebra $\\mathcal{RH}om_{\\mathcal{O}_Y}(\\mathcal{O}_X, \\mathcal{O}_X)$ is isomorphic to the universal enveloping algebra of the shifted normal bundle $\\mathrm{N}_{X/Y}[-1]$ endowed with a specific Lie structure, strengthening an earlier result of C\\u{a}ld\\u{a}raru, Tu, and the first author This "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09402","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"}