{"paper":{"title":"Sufficient Conditions for Holomorphic Linearisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CV","authors_text":"Finnur Larusson, Frank Kutzschebauch, Gerald W. Schwarz","submitted_at":"2015-03-03T01:07:54Z","abstract_excerpt":"Let $G$ be a reductive complex Lie group acting holomorphically on $X={\\mathbb C}^n$. The (holomorphic) Linearisation Problem asks if there is a holomorphic change of coordinates on ${\\mathbb C}^n$ such that the $G$-action becomes linear. Equivalently, is there a $G$-equivariant biholomorphism $\\Phi\\colon X\\to V$ where $V$ is a $G$-module? There is an intrinsic stratification of the categorical quotient $Q_X$, called the Luna stratification, where the strata are labeled by isomorphism classes of representations of reductive subgroups of $G$. Suppose that there is a $\\Phi$ as above. Then $\\Phi$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00794","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"}