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
$f$ 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.sponsorship | Bolsa Pesquisador Visitante Especial (PVE) - Ciˆencias sem Fronteiras/CNPq Project number: 401947/2013-0
DGICYT Grant MTM2015–64013–P
CNPq Project number 401947/2013-0 | en_US |
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 |