{"paper":{"title":"Finite determinacy of matrices over local rings. Tangent modules to the miniversal deformation for R-linear group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Dmitry Kerner, Genrich Belitskii","submitted_at":"2015-01-28T16:12:29Z","abstract_excerpt":"We consider matrices with entries in a local ring, Mat(m,n,R). Fix a group action, G on Mat(m,n,R), and a subset of allowed deformations, \\Sigma\\subseteq Mat(m,n,R). The standard question of Singularity Theory is the finite-(\\Sigma,G)-determinacy of matrices. Finite determinacy implies algebraizability and is equivalent to a stronger notion: stable algebraizability.\n  In our previous work this determinacy question was reduced to the study of the tangent spaces to \\Sigma and to the orbit, T_{(\\Sigma,A)}, T_{(GA,A)} , and their quotient, the tangent module to the miniversal deformation. In parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07168","kind":"arxiv","version":4},"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"}