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

2024/07/03 by Carles Bivià-Ausina, Bivià-Ausina, Carles, Konstantinos Kourliouros +3
Computer Science · Mathematics · #32S05 #32S50 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2407.02947

openalex publication_date 2024/07/03 · openalex created_date 2024/07/06 · openalex updated_date 2026/07/28

Abstract

We introduce the module of derivations Θ_h,M attached to a given analytic map h:(\mathbb Cⁿ,0)→ (\mathbb C^p,0) and a submodule M⊆ \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 Cⁿ,0)→ (\mathbb C^q,0). In particular, if X is an analytic subvariety of \mathbb Cⁿ, we derive expressions for analytic invariants defined in terms of the module Θ_X of logarithmic vector fields of X.

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