dc.contributor.author Fernández de Bobadilla, J. dc.contributor.author Nuño-Ballesteros, J.J. dc.contributor.author Peñafort Sanchis, Guillermo dc.date.accessioned 2019-01-10T17:20:06Z dc.date.available 2019-01-10T17:20:06Z dc.date.issued 2019 dc.identifier.issn 1139-1138 dc.identifier.uri http://hdl.handle.net/20.500.11824/910 dc.description.abstract Let $f:(\mathbb C^n,S)\to (\mathbb C^{n+1},0)$ be a germ whose image is given by $g=0$. We define an $\mathcal O_{n+1}$-module $M(g)$ with the property that $\mathscr A_e$-$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, with equality if en_US $f$ is weighted homogeneous. We also define a relative version $M_y(G)$ for unfoldings $F$, in such a way that $M_y(G)$ specialises to $M(g)$ when $G$ specialises to $g$. The main result is that if $(n,n+1)$ are nice dimensions, then $\dim_\mathbb C M(g)\ge \mu_I(f)$, with equality if and only if $M_y(G)$ is Cohen-Macaulay, for some stable unfolding $F$. Here, $\mu_I(f)$ denotes the image Milnor number of $f$, so that if $M_y(G)$ is Cohen-Macaulay, then Mond's conjecture holds for $f$; furthermore, if $f$ is weighted homogeneous, Mond's conjecture for $f$ is equivalent to the fact that $M_y(G)$ is Cohen-Macaulay. Finally, we observe that to prove Mond's conjecture, it is enough to prove it in a suitable family of examples. dc.description.sponsorship Bolsa Pesquisador Visitante Especial (PVE) - Ciˆencias sem Fronteiras/CNPq Project number: 401947/2013-0 en_US DGICYT Grant MTM2015–64013–P CNPq Project number 401947/2013-0 dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Image Milnor number, Ae-codimension, weighted homogeneous. en_US dc.title A jacobian module for disentanglements and applications to Mond's conjecture en_US dc.type info:eu-repo/semantics/bookPart en_US dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/615655 en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/publishedVersion en_US dc.journal.title Revista Matemática Complutense en_US
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