{"paper":{"title":"A-classification of map-germs via $_V$K-equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kevin Houston, Roberta Wik Atique","submitted_at":"2013-02-05T16:40:34Z","abstract_excerpt":"The classification of map-germs up to the natural right-left equivalence (also known as A-equivalence) is often complicated. Certainly it is more complicated than K-equivalence which is extremely easy to work with because the associated tangent spaces are not 'mixed' modules as they are in the A-equivalence case.\n  In this paper we use a version of K-equivalence, denoted $_V$K-equivalence, that is defined using K-equivalences that preserve a variety in the source of maps to classify maps up to A-equivalence. This is possible through making clear the connection between the two equivalences - pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1104","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"}