{"paper":{"title":"The Koszul complex of a moment map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.SG","authors_text":"Gerald W. Schwarz, Hans-Christian Herbig","submitted_at":"2012-05-21T14:13:00Z","abstract_excerpt":"Let $K\\to U(V)$ be a unitary representation of the compact Lie group $K$. Then there is a canonical moment mapping $\\rho\\colon V\\to\\mathfrak k^*$. We have the Koszul complex ${\\mathcal K}(\\rho,\\mathcal C^\\infty(V))$ of the component functions $\\rho_1,...,\\rho_k$ of $\\rho$. Let $G=K_{\\mathbb C}$, the complexification of $K$. We show that the Koszul complex is a resolution of the smooth functions on $\\rho^{-1}(0)$ if and only if $G\\to\\GL(V)$ is 1-large, a concept introduced in earlier work of the second author. Now let $M$ be a symplectic manifold with a Hamiltonian action of $K$. Let $\\rho$ be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4608","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":""},"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"}