Modules of derivations, logarithmic ideals and singularities of maps on analytic varieties
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913415941849088 |
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| author | Bivià-Ausina, Carles Kourliouros, Konstantinos Ruas, Maria Aparecida Soares |
| author_facet | Bivià-Ausina, Carles Kourliouros, Konstantinos Ruas, Maria Aparecida Soares |
| contents | We introduce the module of derivations $Θ_{h,M}$ 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 $Θ_{h,M}$. Moreover, we obtain formulas for several numerical invariants associated to the pair $(h,M)$ and a given analytic map germ $f:(\mathbb C^n,0)\to (\mathbb C^q,0)$. In particular, if $X$ is an analytic subvariety of $\mathbb C^n$, we derive expressions for analytic invariants defined in terms of the module $Θ_X$ of logarithmic vector fields of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modules of derivations, logarithmic ideals and singularities of maps on analytic varieties Bivià-Ausina, Carles Kourliouros, Konstantinos Ruas, Maria Aparecida Soares Algebraic Geometry Commutative Algebra Complex Variables 32S05, 32S50 We introduce the module of derivations $Θ_{h,M}$ 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 $Θ_{h,M}$. Moreover, we obtain formulas for several numerical invariants associated to the pair $(h,M)$ and a given analytic map germ $f:(\mathbb C^n,0)\to (\mathbb C^q,0)$. In particular, if $X$ is an analytic subvariety of $\mathbb C^n$, we derive expressions for analytic invariants defined in terms of the module $Θ_X$ of logarithmic vector fields of $X$. |
| title | Modules of derivations, logarithmic ideals and singularities of maps on analytic varieties |
| topic | Algebraic Geometry Commutative Algebra Complex Variables 32S05, 32S50 |
| url | https://arxiv.org/abs/2407.02947 |