{"paper":{"title":"Image Milnor number and $\\mathscr{A}_e$-codimension for maps between weighted homogeneous irreducible curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Daiane Alice Henrique Ament, Jo\\~ao Nivaldo Tomazella, Juan Jose Nu\\~no Ballesteros","submitted_at":"2017-09-27T13:36:51Z","abstract_excerpt":"Let $(X,0)\\subset (\\mathbb{C}^n,0)$ be an irreducible weighted homogeneous singularity curve and let $f:(X,0)\\to(\\mathbb{C}^2,0)$ be a map germ finite, one-to-one and weighted homogeneous with the same weights of $(X,0)$. We show that $\\mathscr{A}_e$-$codim(X,f)=\\mu_I(f)$, where $\\mathscr{A}_e$-$codim(X,f)$ is the $\\mathscr{A}_e$-codimension, i.e., the minimum number of parameters in a versal deformation and $\\mu_I(f)$ is the image Milnor number, i.e., the number of vanishing cycles in the image of a stabilisation of $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09504","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"}