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dc.contributor.authorFernández de Bobadilla J.en_US
dc.contributor.authorNuño Ballesteros J. J.en_US
dc.contributor.authorPeñafort Sanchis G.en_US
dc.date.accessioned2019-01-10T17:20:06Z
dc.date.available2019-01-10T17:20:06Z
dc.date.issued2019
dc.identifier.issn1139-1138
dc.identifier.urihttp://hdl.handle.net/20.500.11824/910
dc.description.abstractLet $f:(\mathbb C^n,S)\to (\mathbb C^{n+1},0)$ 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 $f$ 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.en_US
dc.description.sponsorshipBolsa Pesquisador Visitante Especial (PVE) - Ciˆencias sem Fronteiras/CNPq Project number: 401947/2013-0 DGICYT Grant MTM2015–64013–P CNPq Project number 401947/2013-0en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherRevista Matemática Complutenseen_US
dc.relationinfo:eu-repo/grantAgreement/EC/FP7/615655en_US
dc.relationES/1PE/SEV-2013-0323en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectImage Milnor number, Ae-codimension, weighted homogeneous.en_US
dc.titleA jacobian module for disentanglements and applications to Mond's conjectureen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/acceptedVersionen_US


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