{"paper":{"title":"Vector fields liftable over finitely determined multigerms of corank at most one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Takashi Nishimura","submitted_at":"2011-12-06T10:10:29Z","abstract_excerpt":"In this paper, we propose one index $i_1(f)-i_2(f)$ which measures how well-behaved a given finitely determined multigerm $f: (\\mathbb{K}^n,S)\\to (\\mathbb{K}^p,0)$ $(n\\le p)$ of corank at most one is from the viewpoint of liftable vector fields; and we answer the following problems when the index indicates that the given multigerm $f$ is best-behaved.\n1) When is the module of vector fields liftable over $f$ finitely generated?\n2) How can we characterize the minimal number of generators when the module of vector fields liftable over $f$ is finitely generated?\n3) How can we calculate the minimal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1214","kind":"arxiv","version":2},"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"}