{"paper":{"title":"Extensions of Poisson Structures on Singular Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Aaron McMillan Fraenkel","submitted_at":"2013-10-23T00:50:12Z","abstract_excerpt":"Fix a codimension-1 affine Poisson variety $(X,\\pi_X)$ in $\\mathbb{C}^n$ with an isolated singularity at the origin. We characterize possible extensions of $\\pi_X$ to $\\mathbb{C}^n$ using the Koszul complex of the Jacobian ideal of $X$. In the particular case of a singular surface, we show that there always exists an extension of $\\pi_X$ to $\\mathbb{C}^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6083","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"}