{"paper":{"title":"On local invariants of singular symplectic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Wojciech Domitrz","submitted_at":"2016-09-10T11:48:03Z","abstract_excerpt":"We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a $2n$-dimensional manifold. In the $\\mathbb C$-analytic category this set consists of the Martinet hypersurface $\\Sigma _2$, the restriction of the singular symplectic form $\\omega$ to $T\\Sigma_2$ and the kernel of $\\omega^{n-1}$ at the point $p\\in \\Sigma_2$. In the $\\mathbb R$-analytic and smooth categories this set contains one more invariant: the canonical orientation of $\\Sigma_2$. We find the conditions to determine the kernel of $\\omega^{n-1}$ at $p$ by the other"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03033","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"}