{"paper":{"title":"A Jacobian module for disentanglements and applications to Mond's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"G. Pe\\~nafort-Sanchis, J. Fern\\'andez de Bobadilla, J. J. Nu\\~no-Ballesteros","submitted_at":"2016-04-08T18:36:28Z","abstract_excerpt":"Given a germ of holomorphic map $f$ from $\\mathbb C^n$ to $\\mathbb C^{n+1}$, we define a module $M(f)$ whose dimension over $\\mathbb C$ is an upper bound for the $\\mathscr A$-codimension of $f$, with equality if $f$ is weighted homogeneous. We also define a relative version $M_y(F)$ of the module, for unfoldings $F$ of $f$. The main result is that if $(n,n+1)$ are nice dimensions, then the dimension of $M(f)$ over $\\mathbb C$ is an upper bound of the image Milnor number of $f$, with equality if and only if the relative module $M_y(F)$ is Cohen-Macaulay for some stable unfolding $F$. In particu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02422","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"}