Modules of derivations, logarithmic ideals and singularities of maps on analytic varieties

[EN] We introduce the module of derivations $\Theta_{h,M}$ attached to a given analytic map $h:(\mathbb C^n,0)\to (\mathbb C^p,0)$ and a submodule $M\subseteq \mathcal O_n^p$ and analyse several exact sequences related to $\Theta_{h,M}$. Moreover, we obtain formulas for several numerical invariants...

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Detalles Bibliográficos
Autores: Bivià-Ausina, Carles|||0000-0003-0784-3353, Kourliouros, Konstantinos, Soares Ruas, Maria Aparecida
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/232697
Acceso en línea:https://riunet.upv.es/handle/10251/232697
Access Level:acceso abierto
Palabra clave:Milnor number
Logarithmic vector fields
Tjurina number
Parameter submodules
Buchsbaum-Rim multiplicity
Descripción
Sumario:[EN] We introduce the module of derivations $\Theta_{h,M}$ attached to a given analytic map $h:(\mathbb C^n,0)\to (\mathbb C^p,0)$ and a submodule $M\subseteq \mathcal O_n^p$ and analyse several exact sequences related to $\Theta_{h,M}$. Moreover, we obtain formulas for several numerical invariants associated to the pair $(h,M)$ and a given analytic map germ $f:(\mathbb C^n,0)\to (\mathbbC^q,0)$. In particular, if $X$ is an analytic subvariety of $\mathbb C^n$, we derive expressions for analytic invariants defined in terms of the module $\Theta_X$ of logarithmic vector fields of $X$.