{"paper":{"title":"Finite determinacy of matrices over local rings.II. Tangent modules to the miniversal deformations for group-actions involving the ring automorphisms","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":"2016-04-21T10:31:29Z","abstract_excerpt":"We consider matrices with entries in a local ring, Mat(m,n;R). Fix an action of group G on Mat(m,n;R), and a subset of allowed deformations, \\Sigma in Mat(m,n;R). The standard question (along the lines of Singularity Theory) is the finite-(\\Sigma,G)-determinacy of matrices.\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 particular, the order of determinacy is controlled by the annihilator of this tangent module.\n  Then"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06247","kind":"arxiv","version":1},"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"}