{"paper":{"title":"Group actions on filtered modules and finite determinacy. Finding large submodules in the orbit by linearization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dmitry Kerner, Genrich Belitskii","submitted_at":"2012-12-31T14:04:05Z","abstract_excerpt":"Fix a module M over a local ring R and a group action G on M, not necessarily R-linear. To understand how large is the G-orbit of an element z\\in M one looks for the large submodules of M lying in Gz. We provide the corresponding (necessary/sufficient) conditions in terms of the tangent space to the orbit, T_{(Gz,z)}.\n  This question originates from the classical finite determinacy problem of Singularity Theory. Our treatment is rather general, in particular we extend the classical criteria of Mather (and many others) to a broad class of rings, modules and group actions.\n  When a particular `d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6894","kind":"arxiv","version":5},"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"}